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All Textbook Solutions for Intermediate Algebra

In the following exercises, solve each system of equations using a matrix. 220. {2y+3z=15x+3y=67x+z=1 In the following exercises, solve each system of equations using a matrix. 221. {3xz=35y+2z=64x+3y=8 In the following exercises, solve each system of equations using a matrix. 222. {2x+3y+z=12x+y+z=93x+4y+2z=20 In the following exercises, solve each system of equations using a matrix. 223. {x+2y+6z=5x+y2z=3x4y2z=1 In the following exercises, solve each system of equations using a matrix. 224. {x+2y3z=1x3y+z=12xy2z=2 In the following exercises, solve each system of equations using a matrix. 225. {4x3y+2z=02x+3y7z=12x2y+3z=6 In the following exercises, solve each system of equations using a matrix. 226. {xy+2z=42x+y+3z=23x+3y6z=12 In the following exercises, solve each system of equations using a matrix. 227. {x3y+2z=14x+2y3z=43x+y2z=6 In the following exercises, solve each system of equations using a matrix. 228. {x+y3z=1yz=0x+2y=1 In the following exercises, solve each system of equations using a matrix. 229. {x+2y+z=4x+y2z=32x3y+z=7 Solve the system of equations {x+y=10xy=6 (a) by graphing and (b) by substitution. (c) Which method do you prefer? Why?Solve the system of equations {3x+y=12x=y8 by substitution and explain all your steps in words.Evaluate the determinate of (a) [5324] (b)[4607] .Evaluate the determinate of (a) [1324] (b) [7350] .For the determinant |114021233| , find and then evaluate the minor of (a) a1 (b) b2 (c) c3 .For the determinant |210301123| , find and then evaluate the minor of (a) a2 (b) b3 (c) c2 .Evaluate the determinant |324012231| , by expanding by minors along the first row.Evaluate the determinant |322214103| , by expanding by minors along the first row.Evaluate the determinant |213034343| by expanding by minors.Evaluate the determinant |213122440| by expanding by minors.Solve using Cramer’s rule: {3x+y=32x+3y=6 .Solve using Cramer’s rule: {x+y=22x+y=4 .Solve the system of equations using Cramer’s Rule: {3x+8y+2z=52x+5y3z=0x+2y2z=1 .Solve the system of equations using Cramer’s Rule: {3x+y6z=32x+6y+3z=03x+2y3z=6 .Solve the system of equations using Cramer’s rule: {4x3y=88x6y=14 .Solve the system of equations using Cramer’s rule: {x=3y+42x+6y=8 .Determine whether the points (3,2),(5,3), and (1,1) are collinear.Determine whether the points (4,1),(6,2) and (2,4) are collinear.In the following exercises, evaluate the determinate of each square matrix. 232. [6231]In the following exercises, evaluate the determinate of each square matrix. 233. [4835]In the following exercises, evaluate the determinate of each square matrix. 234. [3504]In the following exercises, evaluate the determinate of each square matrix. 235. [2075]In the following exercises, find and then evaluate the indicated minors. 236. |314102415| Find the minor (a) a1 (b) b2 (c)c3 In the following exercises, find and then evaluate the indicated minors. 237. |132421203| Find the minor (a) a1 (b) b1 (c) c2 In the following exercises, find and then evaluate the indicated minors. 238. |234123012| Find the minor (a) a2 (b) b2 (c) c2 In the following exercises, find and then evaluate the indicated minors. 239. |223130232| Find the minor (a) a3 (b) b3 (c) c3 In the following exercises, evaluate each determinant by expanding by minors along the first row. 240. |231122313|In the following exercises, evaluate each determinant by expanding by minors along the first row. 241. |412321257|In the following exercises, evaluate each determinant by expanding by minors along the first row. 242. |234567120|In the following exercises, evaluate each determinant by expanding by minors along the first row. 243. |132564021|In the following exercises, evaluate each determinant by expanding by minors. 244. |514403226|In the following exercises, evaluate each determinant by expanding by minors. 245. |413322104|In the following exercises, evaluate each determinant by expanding by minors. 246. |354130261|In the following exercises, evaluate each determinant by expanding by minors. 247. |243514320|In the following exercises, solve each system of equations using Cramer’s Rule. 248. {2x+3y=3x+3y=12 In the following exercises, solve each system of equations using Cramer’s Rule. 249. {x2y=52x3y=4 In the following exercises, solve each system of equations using Cramer’s Rule. 250. {x3y=92x+5y=4 In the following exercises, solve each system of equations using Cramer’s Rule. 251. {2x+y=43x2y=6 In the following exercises, solve each system of equations using Cramer’s Rule. 252. {x2y=52x3y=4 In the following exercises, solve each system of equations using Cramer’s Rule. 253. {x3y=92x+5y=4 In the following exercises, solve each system of equations using Cramer’s Rule. 254. {5x3y=12xy=2 In the following exercises, solve each system of equations using Cramer’s Rule. 255. {3x+8y=32x+5y=3 In the following exercises, solve each system of equations using Cramer’s Rule. 256. {6x5y+2z=32x+y4z=53x3y+z=1 In the following exercises, solve each system of equations using Cramer’s Rule. 257. {4x3y+z=72x5y4z=33x2y2z=7 In the following exercises, solve each system of equations using Cramer’s Rule. 258. {2x5y+3z=83xy+4z=7x+3y+2z=3 In the following exercises, solve each system of equations using Cramer’s Rule. 259. {11x+9y+2z=97x+5y+3z=74x+3y+z=3 In the following exercises, solve each system of equations using Cramer’s Rule. 260. {x+2z=04y+3z=22x5y=3 In the following exercises, solve each system of equations using Cramer’s Rule. 261. {2x+5y=43yz=34x+3z=3 In the following exercises, solve each system of equations using Cramer’s Rule. 262. {2y+3z=15x+3y=67x+z=1 In the following exercises, solve each system of equations using Cramer’s Rule. 263. {3xz=35y+2z=64x+3y=8 In the following exercises, solve each system of equations using Cramer’s Rule. 264. {2x+y=36x+3y=9 In the following exercises, solve each system of equations using Cramer’s Rule. 265. {x4y=13x+12y=3 In the following exercises, solve each system of equations using Cramer’s Rule. 266. {3xy=46x+2y=16 In the following exercises, solve each system of equations using Cramer’s Rule. 267. {4x+3y=220x+15y=5 In the following exercises, solve each system of equations using Cramer’s Rule. 268. {x+y3z=1yz=0x+2y=1 In the following exercises, solve each system of equations using Cramer’s Rule. 269. {2x+3y+z=12x+y+z=93x+4y+2z=20 In the following exercises, solve each system of equations using Cramer’s Rule. 270. {3x+4y3z=22x+3yz=12x+y2z=6 In the following exercises, solve each system of equations using Cramer’s Rule. 271. {x2y+3z=1x+y3z=73x4y+5z=7 In the following exercises, determine whether the given points are collinear. 272. (0,1),(2,0), and (2,2) .In the following exercises, determine whether the given points are collinear. 273. (0,5),(2,2), and (2,8) .In the following exercises, determine whether the given points are collinear. 274. (4,3),(6,4), and (2,2)In the following exercises, determine whether the given points are collinear. 275. (2,1),(4,4), and (0,2)Explain the difference between a square matrix and its determinant. Give an example of each.Explain what is meant by the minor of an entry in a square matrix.Explain how to decide which row or column you will use to expand a 33 determinant.Explain the steps for solving a system of equations using Cramer’s rule.Determine whether the ordered pair is a solution to the system: {x5y102x+3y2 . (a) (3,1) (b) (6,3)Determine whether the ordered pair is a solution to the system: {y4x24xy20 . (a) (2,1) (b) (4,1)Solve the system by graphing: {y3x+2yx1 .Solve the system by graphing: {y 1 2x+3y3x4 .Solve the system by graphing: {x+y2y 2 3x1 .Solve the system by graphing: {3x2y6y 1 4x+5 .Solve the system by graphing: {y3x2y1 .Solve the system by graphing: {x4x2y4 .Solve the system by graphing: {3x2y12y 3 2x+1 .Solve the system by graphing: {x+3y8y 1 3x2 .Solve the system by graphing: {y3x+13x+y4 .Solve the system by graphing: {y 1 4x+2x+4y4 .A trailer can carry a maximum weight of 160 pounds and a maximum volume of 15 cubic feet. A microwave oven weighs 30 pounds and has 2 cubic feet of volume, while a printer weighs 20 pounds and has 3 cubic feet of space. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could 4 microwaves and 2 printers be carried on this trailer? (d) Could 7 microwaves and 3 printers be carried on this trailer?Mary needs to purchase supplies of answer sheets and pencils for a standardized test to be given to the juniors at her high school. The number of the answer sheets needed is at least 5 more than the number of pencils. The pencils cost $2 and the answer sheets cost $1. Mary’s budget for these supplies allows for a maximum cost of $400. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could Mary purchase 100 pencils and 100 answer sheets? (d) Could Mary purchase 150 pencils and 150 answer sheets?Tension needs to eat at least an extra 1,000 calories a day to prepare for running a marathon. He has only $25 to spend on the extra food he needs and will spend it on $0.75 donuts which have 360 calories each and $2 energy drinks which have 110 calories. (a) Write a system of inequalities that models this situation. (b) Graph the system. (c) Can he buy 8 donuts and 4 energy drinks and satisfy his caloric needs? (d) Can he buy 1 donut and 3 energy drinks and satisfy his caloric needs?Philip’s doctor tells him he should add at least 1,000 more calories per day to his usual diet. Philip wants to buy protein bars that cost $1.80 each and have 140 calories and juice that costs $1.25 per bottle and have 125 calories. He doesn’t want to spend more than $12. (a) Write a system of inequalities that models this situation. (b) Graph the system. (c) Can he buy 3 protein bars and 5 bottles of juice? (d) Can he buy 5 protein bars and 3 bottles of juice?In the following exercises, determine whether each ordered pair is a solution to the system. 280. {3x+y52xy10 (a) (3,3) (b) (7,1)In the following exercises, determine whether each ordered pair is a solution to the system. 281. {4xy102x+2y8 (a) (5,2) (b) (1,3)In the following exercises, determine whether each ordered pair is a solution to the system. 282. {y 2 3x5x+ 1 2y4 (a) (6,4) (b) (3,0)In the following exercises, determine whether each ordered pair is a solution to the system. 283. {y 3 2x+3 3 4x2y5 (a) (4,1) (b) (8,3)In the following exercises, determine whether each ordered pair is a solution to the system. 284. {7x+2y145xy8 (a) (2,3) (b) (7,1)In the following exercises, determine whether each ordered pair is a solution to the system. 285. {6x5y202x+7y8 (a) (1,3) (b) (4,4)In the following exercises, solve each system by graphing. 286. {y3x+2yx1 In the following exercises, solve each system by graphing. 287. {y2x+2yx1 In the following exercises, solve each system by graphing. 288. {y2x1y 1 2x+4 In the following exercises, solve each system by graphing. 289. {y 2 3x+2y2x3 In the following exercises, solve each system by graphing. 290. {xy1y 1 4x+3 In the following exercises, solve each system by graphing. 291. {x+2y4yx2 In the following exercises, solve each system by graphing. 292. {3xy6y 1 2x In the following exercises, solve each system by graphing. 293. {2x+4y8y 3 4x In the following exercises, solve each system by graphing. 294. {2x5y103x+4y12 In the following exercises, solve each system by graphing. 295. {3x2y64x2y8 In the following exercises, solve each system by graphing. 296. {2x+2y4x+3y9 In the following exercises, solve each system by graphing. 297. {2x+y6x+2y4 In the following exercises, solve each system by graphing. 298. {x2y3y1 In the following exercises, solve each system by graphing. 299. {x3y4y1 In the following exercises, solve each system by graphing. 300. {y 1 2x3x2 In the following exercises, solve each system by graphing. 301. {y 2 3x+5x3 In the following exercises, solve each system by graphing. 302. {y 3 4x2y2 In the following exercises, solve each system by graphing. 303. {y 1 2x+3y1 In the following exercises, solve each system by graphing. 304. {3x4y8x1 In the following exercises, solve each system by graphing. 305. {3x+5y10x1 In the following exercises, solve each system by graphing. 306. {x3y2 In the following exercises, solve each system by graphing. 307. {x1y3 In the following exercises, solve each system by graphing. 308. {2x+4y4y 1 2x2 In the following exercises, solve each system by graphing. 309. {x3y6y 1 3x+1 In the following exercises, solve each system by graphing. 310. {2x+6y06y2x+4 In the following exercises, solve each system by graphing. 311. {3x+6y124y2x4 In the following exercises, solve each system by graphing. 312. {y3x+23x+y5 In the following exercises, solve each system by graphing. 313. {y 1 2x12x+4y4 In the following exercises, solve each system by graphing. 314. {y 1 4x2x+4y6 In the following exercises, solve each system by graphing. 315. {y3x13x+y4 In the following exercises, solve each system by graphing. 316. {3yx+22x+6y8 In the following exercises, solve each system by graphing. 317. {y 3 4x23x+4y7 In the following exercises, translate to a system of inequalities and solve. 318. Caitlyn sells her drawings at the county fair. She wants to sell at least 60 drawings and has portraits and landscapes. She sells the portraits for $15 and the landscapes for $10. She needs to sell at least $800 worth of drawings in order to earn a profit. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Will she make a profit if she sells 20 portraits and 35 landscapes? (d) Will she make a profit if she sells 50 portraits and 20 landscapes?In the following exercises, translate to a system of inequalities and solve. 319. Jake does not want to spend more than $50 on bags of fertilizer and peat moss for his garden. Fertilizer costs $2 a bag and peat moss costs $5 a bag. Jake’s van can hold at most 20 bags. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can he buy 15 bags of fertilizer and 4 bags of peat moss? (d) Can he buy 10 bags of fertilizer and 10 bags of peat moss?In the following exercises, translate to a system of inequalities and solve. 320. Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is $7. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she mail 60 cards and 26 packages? (d) Can she mail 90 cards and 40 packages?In the following exercises, translate to a system of inequalities and solve. 321. Juan is studying for his final exams in chemistry and algebra. he knows he only has 24 hours to study, and it will take him at least three times as long to study for algebra than chemistry. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can he spend 4 hours on chemistry and 20 hours on algebra? (d) Can he spend 6 hours on chemistry and 18 hours on algebra?In the following exercises, translate to a system of inequalities and solve. 322. Jocelyn is pregnant and so she needs to eat at least 500 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.35 each and the granola bars cost $2.50 each. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could she buy 5 bananas and 6 granola bars? (d) Could she buy 3 bananas and 4 granola bars?In the following exercises, translate to a system of inequalities and solve. 323. Mark is attempting to build muscle mass and so he needs to eat at least an additional 80 grams of protein a day. A bottle of protein water costs $3.20 and a protein bar costs $1.75. The protein water supplies 27 grams of protein and the bar supplies 16 gram. If he has $10 dollars to spend (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could he buy 3 bottles of protein water and 1 protein bar? (d) Could he buy no bottles of protein water and 5 protein bars?In the following exercises, translate to a system of inequalities and solve. 324. Jocelyn desires to increase both her protein consumption and caloric intake. She desires to have at least 35 more grams of protein each day and no more than an additional 200 calories daily. An ounce of cheddar cheese has 7 grams of protein and 110 calories. An ounce of parmesan cheese has 11 grams of protein and 22 calories. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could she eat 1 ounce of cheddar cheese and 3 ounces of parmesan cheese? (d) Could she eat 2 ounces of cheddar cheese and 1 ounce of parmesan cheese?In the following exercises, translate to a system of inequalities and solve. 325. Mark is increasing his exercise routine by running and walking at least 4 miles each day. His goal is to burn a minimum of 1500 calories from this exercise. Walking burns 270 calories/mile and running burns 650 calories. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Could he meet his goal by walking 3 miles and running 1 mile? (d) Could he his goal by walking 2 miles and running 2 mile Graph the inequality xy3 . How do you knowwhich side of the line xy=3 should be shaded?Graph the system {x+2y6y 1 2x4 . What does the solution mean?In the following exercises, determine if the following points are solutions to the given system of equations. 328. {x+3y=92x4y=12 (a) (3,2) (b) (0,3)In the following exercises, determine if the following points are solutions to the given system of equations. 329. {x+y=8y=x4 (a) (6,2) (b) (9,1)In the following exercises, solve the following systems of equations by graphing. 330. {3x+y=6x+3y=6 In the following exercises, solve the following systems of equations by graphing. 331. {x+4y=1x=3 In the following exercises, solve the following systems of equations by graphing. 332. {2xy=54x2y=10 In the following exercises, solve the following systems of equations by graphing. 333. {x+2y=4y= 1 2x3 In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 334. {y= 2 5x+22x+5y=10 In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 335. {3x+2y=6y=3x+4 In the following exercises, without graphing determine the number of solutions and then classify the system of equations. 336. {5x4y=0y= 5 4x5 In the following exercises, solve the systems of equations by substitution. 337. {3x2y=2y= 1 2x+3 In the following exercises, solve the systems of equations by substitution. 338. {xy=02x+5y=14 In the following exercises, solve the systems of equations by substitution. 339. {y=2x+7y= 2 3x1 In the following exercises, solve the systems of equations by substitution. 340. {y=5x5x+y=6 In the following exercises, solve the systems of equations by substitution. 341. {y= 1 3x+2x+3y=6 In the following exercises, solve the systems of equations by elimination 342. {x+y=12xy=10 In the following exercises, solve the systems of equations by elimination 343. {3x8y=20x+3y=1 In the following exercises, solve the systems of equations by elimination 344. {9x+4y=25x+3y=5 In the following exercises, solve the systems of equations by elimination 345. { 1 3x 1 2y=1 3 4xy= 5 2 In the following exercises, solve the systems of equations by elimination 346. {x+3y=82x6y=20 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 347. {6x5y=273x+10y=24 In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination. 348. {y=3x94x5y=23 In the following exercises, translate to a system of equations and solve. 349. Mollie wants to plant 200 bulbs in her garden, all irises and tulips. She wants to plant three times as many tulips as irises. How many irises and how many tulips should she plant?In the following exercises, translate to a system of equations and solve. 350. Ashanti has been offered positions by two phone companies. The first company pays a salary of $22,000 plus a commission of $100 for each contract sold. The second pays a salary of $28,000 plus a commission of $25 for each contract sold. How many contract would need to be sold to make the total pay the same?In the following exercises, translate to a system of equations and solve. 351. Leroy spent 20 minutes jogging and 40 minutes cycling and burned 600 calories. The next day, Leroy swapped times, doing 40 minutes of jogging and 20 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?In the following exercises, translate to a system of equations and solve. 352. Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and calculator. Troy bought four notebooks and five calculators for $116. Lisa bought two notebooks and three calculators for $68. Find the cost of each notebook and each thumb drive.In the following exercises, translate to a system of equations and solve. 353. The difference of two supplementary angles is 58 degrees. Find the measures of the angles.In the following exercises, translate to a system of equations and solve. 354. Two angles are complementary. The measure of the larger angle is five more than four times the measure of the smaller angle. Find the measures of both angles.In the following exercises, translate to a system of equations and solve. 355. The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.In the following exercises, translate to a system of equations and solve. 356. Becca is hanging a 28 foot floral garland on the two sides and top of a pergola to prepare for a wedding. The height is four feet less than the width. Find the height and width of the pergola.In the following exercises, translate to a system of equations and solve. 357. The perimeter of a city rectangular park is 1428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.In the following exercises, translate to a system of equations and solve. 358. Sheila and Lenore were driving to their grandmother’s house. Lenore left one hour after Sheila. Sheila drove at a rate of 45 mph, and Lenore drove at a rate of 60 mph. How long will it take for Lenore to catch up to Sheila?In the following exercises, translate to a system of equations and solve. 359. Bob left home, riding his bike at a rate of 10 miles per hour to go to the lake. Cheryl, his wife, left 45 minutes ( 34 hour) later, driving her car at a rate of 25 miles per hour. How long will it take Cheryl to catch up to Bob?In the following exercises, translate to a system of equations and solve. 360. Marcus can drive his boat 36 miles down the river in three hours but takes four hours to return upstream. Find the rate of the boat in still water and the rate of the current.In the following exercises, translate to a system of equations and solve. 361. A passenger jet can fly 804 miles in 2 hours with a tailwind but only 776 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.For the following exercises, translate to a system of equations and solve. 362. Lynn paid a total of $2,780 for 261 tickets to the theater. Student tickets cost $10 and adult tickets cost $15. How many student tickets and how many adult tickets did Lynn buy?For the following exercises, translate to a system of equations and solve. 363. Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?For the following exercises, translate to a system of equations and solve. 364. Yumi wants to make 12 cups of party mix using candies and nuts. Her budget requires the party mix to cost her $1.29 per cup. The candies are $2.49 per cup and the nuts are $0.69 per cup. How many cups of candies and how many cups of nuts should she use?For the following exercises, translate to a system of equations and solve. 365. A scientist needs 70 liters of a 40% solution ofalcohol. He has a 30% and a 60% solution available. How many liters of the 30% and how many liters of the 60% solutions should he mix to make the 40% solution?For the following exercises, translate to a system of equations and solve. 366. Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into CD account that earns 9% per year. How much money should he put into each account?For the following exercises, translate to a system of equations and solve. 367. When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?In the following exercises, determine whether the ordered triple is a solution to the system. 368. {3x4y3z=22x6y+z=32x+3y2z=3 (a) (2,3,1) (b) (3,1,3)In the following exercises, determine whether the ordered triple is a solution to the system. 369. {y= 2 3x2x+3yz=15x3y+z=2 (a) (6,5,12) (b) (5,43,3)In the following exercises, solve the system of equations. 370. {3x5y+4z=55x+2y+z=02x+3y2z=3 In the following exercises, solve the system of equations. 371. {x+ 5 2y+z=22x+2y+ 1 2z=4 1 3xyz=1 In the following exercises, solve the system of equations. 372. {5x+3y=62y+3z=17x+z=1 In the following exercises, solve the system of equations. 373. {2x+3y+z=12x+y+z=93x+4y+2z=20 In the following exercises, solve the system of equations. 374. {x3y+2z=14x+2y3z=43x+y2z=6 After attending a major league baseball game, the patrons often purchase souvenirs. If a family purchases 4 t-shirts, a cap and 1 stuffed animal their total is $135. A couple buys 2 t-shirts, a cap and 3 stuffed animals for their nieces and spends $115. Another couple buys 2 t-shirts, a cap and 1 stuffed animal and their total is $85. What is the cost of each item?Write each system of linear equations as an augmented matrix. 376. {3xy=12x+2y=5 Write each system of linear equations as an augmented matrix. 377. {4x+3y=2x2y3z=72xy+2z=6 Write the system of equations that that corresponds to the augmented matrix. 378. [2433| 2 1]Write the system of equations that that corresponds to the augmented matrix. 379. [103120012| 1 23]In the following exercises, perform the indicated operations on the augmented matrices. 380. [4632| 31] (a) Interchange rows 2 and 1. (b) Multiply row 1 by 4. (c) Multiply row 2 by 3 and add to row 1.In the following exercises, perform the indicated operations on the augmented matrices. 381. [132221423|4 3 1] (a) Interchange rows 2 and 3. (b) Multiply row 1 by 2. (c) Multiply row 3 by -2 and add to row 2.In the following exercises, solve each system of equations using a matrix. 382. {4x+y=6xy=4 In the following exercises, solve each system of equations using a matrix. 383. {2xy+3x=3x+2yz=10x+y+z=5 In the following exercises, solve each system of equations using a matrix. 384. {2y+3z=15x+3y=67x+z=1 In the following exercises, solve each system of equations using a matrix. 385. {x+2y3z=1x3y+z=12xy2z=2 In the following exercises, solve each system of equations using a matrix. 386. {x+y3z=1yz=0x+2y=1 In the following exercise, evaluate the determinate of the square matrix. 387. [8453]In the following exercise, find and then evaluate the indicated minors. 388. |132421203| ; Find the minor (a) a1 (b) b1 (c) c2 In the following exercise, evaluate each determinant by expanding by minors along the first row. 389. |234567120|In the following exercise, evaluate each determinant by expanding by minors. 390. |354130261|In the following exercises, solve each system of equations using Cramer’s rule 391. {x3y=92x+5y=4 In the following exercises, solve each system of equations using Cramer’s rule 392. {4x3y+z=72x5y4z=33x2y2z=7 In the following exercises, solve each system of equations using Cramer’s rule 393. {2x+5y=43yz=34x+3z=3 In the following exercises, solve each system of equations using Cramer’s rule 394. {x+y3z=1yz=0x+2y=1 In the following exercises, solve each system of equations using Cramer’s rule 395. {3x+4y3z=22x+3yz=12x+y2z=6 In the following exercises, determine whether the given points are collinear. 396. (0,2),(1,1), and (2,4)In the following exercises, determine whether each ordered pair is a solution to the system. 397. {4x+y63xy12 (a) (2,1) (b) (3,2)In the following exercises, determine whether each ordered pair is a solution to the system. 398. {y 1 3x+2x 1 4y10 (a) (6,5) (b)(15,8)In the following exercises, solve each system by graphing. 399. {y3x+1yx2 In the following exercises, solve each system by graphing. 400. {xy1y 1 3x2 In the following exercises, solve each system by graphing. 401. {2x3y63x+4y12 In the following exercises, solve each system by graphing. 402. {y 3 4x+1x5 In the following exercises, solve each system by graphing. 403. {x+3y5y 1 3x+6 In the following exercises, solve each system by graphing. 404. {y2x56x+3y4 In the following exercises, translate to a system of inequalities and solve. 405. Roxana makes bracelets and necklaces and sells them at the farmers’ market. She sells the bracelets for $12 each and the necklaces for $18 each. At the market next weekend she will have room to display no more than 40 pieces, and she needs to sell at least $500 worth in order to earn a profit. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Should she display 26 bracelets and 14 necklaces? (d) Should she display 39 bracelets and 1 necklace?In the following exercises, translate to a system of inequalities and solve. 406. Annie has a budget of $600 to purchase paperback books and hardcover books for her classroom. She wants the number of hardcover to be at least 5 more than three times the number of paperback books. Paperback books cost $4 each and hardcover books cost $15 each. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she buy 8 paperback books and 40 hardcover books? (d) Can she buy 10 paperback books and 37 hardcover books?In the following exercises, solve the following systems by graphing. 407. {xy=5x+2y=4 In the following exercises, solve the following systems by graphing. 408. {xy2y3x+1 In the following exercises, solve each system of equations. Use either substitution or elimination. 409. {x+4y=62x+y=3 In the following exercises, solve each system of equations. Use either substitution or elimination. 410. {3x+4y=25x5y=23 In the following exercises, solve each system of equations. Use either substitution or elimination. 411. {x+yz=12xy+2z=83x+2y+z=9 Solve the system of equations using a matrix. 412. {2x+y=7x2y=6 Solve the system of equations using a matrix. 413. {3x+y+z=4x+2y2z=12xyz=1 Solve using Cramer’s rule. 414. {3x+y=32x+3y=6 Solve using Cramer’s rule. 415. Evaluate the determinant by expanding by minors: |322214103|In the following exercises, translate to a system of equations and solve. 416. Greg is paddling his canoe upstream, against the current, to a fishing spot 10 miles away. If he paddles upstream for 2.5 hours and his return trip takes 1.25 hours, find the speed of the current and his paddling speed in still water.In the following exercises, translate to a system of equations and solve. 417. A pharmacist needs 20 liters of a 2% saline solution. He has a 1% and a 5% solution available. How many liters of the 1% and how many liters of the 5% solutions should she mix to make the 2% solution?In the following exercises, translate to a system of equations and solve. 418. Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?In the following exercises, translate to a system of equations and solve. 419. The church youth group is selling snacks to raise money to attend their convention. Amy sold 2 pounds of candy, 3 boxes of cookies and 1 can of popcorn for a total sales of $65. Brian sold 4 pounds of candy, 6 boxes of cookies and 3 cans of popcorn for a total sales of $140. Paulina sold 8 pounds of candy, 8 boxes of cookies and 5 can of popcorn for a total sales of $250. What is the cost of each item?In the following exercises, translate to a system of equations and solve. 420. The manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x granola bars are manufactured (b) Find the revenue function R when x granola bars are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.In the following exercises, translate to a system of equations and solve. 421. Translate to a system of inequalities and solve. Andi wants to spend no more than $50 on Halloween treats. She wants to buy candy bars that cost $1 each and lollipops that cost $0.50 each, and she wants the number of lollipops to be at least three times the number of candy bars. (a) Write a system of inequalities to model this situation. (b) Graph the system. (c) Can she buy 20 candy bars and 40 lollipops?Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial. (a) 5 (b) 8y37y2y3 (c) 3x2y5xy+9xy3 (d) 81m24n2 (e) 3x6y3z Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial. (a) 64k38 (b) 9m3+4m22 (c) 56 (d) 8a47a3b6a2b24ab3+7b4 (e) p4q3 Add or subtract: (a) 12q2+9q2 (b) 8mn3(5mn3) .Add or subtract: (a) 15c2+8c2 (b) 15y2z3(5y2z3) .Add: (a) 8y2+3z23y2 (b) m2n28m2+4n2 .Add: (a) 3m2+n27m2 (b) pq26p5q2 .Find the sum: (7x24x+5)+(x27x+3) .Find the sum: (14y2+6y4)+(3y2+8y+5) .Find the difference: (8x2+3x19)(7x214) .Find the difference: (9b25b4)(3b25b7) .Subtract (a2+5ab6b2) from (a2+b2) .Subtract (m27mn3n2) from (m2+n2) .Find the sum: (3x24xy+5y2)+(2x2xy) .Find the sum: (2x23xy2y2)+(5x23xy) .Simplify: (x3x2y)(xy2+y3)+(x2y+xy2) .Simplify: (p3p2q)+(pq2+q3)(p2q+pq2) .For the function f(x)=3x2+2x15 , find (a) f(3) (b) f(5) (c) f(0) .For the function g(x)=5x2x4 , find (a) g(2) (b) g(1) (c) g(0) .The polynomial function h(t)=16t2+150 gives the height of a stone t seconds after it is dropped from a 150-foot tall cliff. Find the height after t=0 seconds (the initial height of the object).The polynomial function h(t)=16t2+175 gives the height of a ball t seconds after it is dropped from a 175-foot tall bridge. Find the height after t=3 seconds.For functions f(x)=2x24x+3 and g(x)=x22x6 , find (a) (f+g)(x) (b) (f+g)(3) (c) (fg)(x) (d) (fg)(2) .For functions f(x)=5x24x1 and g(x)=x2+3x+8 , find (a) (f+g)(x) (b) (f+g)(3) (c) (fg)(x) (d) (fg)(2) .In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 1. (a) 47x517x2y3+y2 (b) 5c3+11c2c8 (c) 59ab+13b (d) 4 (e) 4pq+17 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 2. (a) x2y2 (b) 13c4 (c) a2+2ab7b2 (d) 4x2y23xy+8 (e) 19 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 3. (a) 8y5x (b) y25yz6z2 (c) y38y2+2y16 (d) 81ab424a2b2+3b (e) 18 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 4. (a) 11y2 (b) 73 (c) 6x23xy+4x2y+y2 (d) 4y2+17z2 (e) 5c3+11c2c8 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 5. (a) 5a2+12ab7b2 (b) 18xy2z (c) 5x+2 (d) y38y2+2y16 (e) 24 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 6. (a) 9y310y2+2y6 (b) 12p3q (c) a2+9ab+18b2 (d) 20x2y210a2b2+30 (e) 17 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 7. (a) 14s29t (b) z25z6 (c) y38y2z+2yz216z3 (d) 23ab214 (e) 3 In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. 8. (a) 15xy (b) 15 (c) 6x23xy+4x2y+y2 (d) 10p9q (e) m4+4m3+6m2+4m+1 In the following exercises, add or subtract the monomials. 9. (a) 7x2+5x2 (b) 4a9a In the following exercises, add or subtract the monomials. 10. (a) 4y3+6y3 (b) y5y In the following exercises, add or subtract the monomials. 11. (a) 12w+18w (b) 7x2y(12x2y)In the following exercises, add or subtract the monomials. 12. (a) 3m+9m (b) 51yz2(8yz2)In the following exercises, add or subtract the monomials. 13. 7x2+5x2+4a9a In the following exercises, add or subtract the monomials. 14. 4y3+6y3y5y In the following exercises, add or subtract the monomials. 15. 12w+18w+7x2y(12x2y)In the following exercises, add or subtract the monomials. 16. 3m+9m+15yz2(8yz2)In the following exercises, add or subtract the monomials. 17. (a) 5b17b (b) 3xy(8xy)+5xy In the following exercises, add or subtract the monomials. 18. (a) 10x35x (b) 17mn2(9mn2)+3mn2 In the following exercises, add or subtract the monomials. 19. (a) 12a+5b22a (b) pq24p3q2 In the following exercises, add or subtract the monomials. 20. (a) 14x3y13x (b) a2b4a5ab2 In the following exercises, add or subtract the monomials. 21. (a) 2a2+b26a2 (b) x2y3x+7xy2 In the following exercises, add or subtract the monomials. 22. (a) 5u2+4v26u2 (b) 12a+8b In the following exercises, add or subtract the monomials. 23. (a) xy25x5y2 (b) 19y+5z In the following exercises, add or subtract the monomials. 24. 12a+5b22a+pq24p3q2 In the following exercises, add or subtract the monomials. 25. 14x3y13x+a2b4a5ab2 In the following exercises, add or subtract the monomials. 26. 2a2+b26a2+x2y3x+7xy2 In the following exercises, add or subtract the monomials. 27. 5u2+4v26u2+12a+8b In the following exercises, add or subtract the monomials. 28. xy25x5y2+19y+5z In the following exercises, add or subtract the monomials. 29. Add: 4a,3b,8a In the following exercises, add or subtract the monomials. 30. Add: 4x,3y,3x In the following exercises, add or subtract the monomials. 31. Subtract 5x6 from 12x6 In the following exercises, add or subtract the monomials. 32. Subtract 2p4 from 7p4 In the following exercises, add the polynomials. 33. (5y2+12y+4)+(6y28y+7)In the following exercises, add the polynomials. 34. (4y2+10y+3)+(8y26y+5)In the following exercises, add the polynomials. 35. (x2+6x+8)+(4x2+11x9)In the following exercises, add the polynomials. 36. (y2+9y+4)+(2y25y1)In the following exercises, add the polynomials. 37. (8x25x+2)+(3x2+3)In the following exercises, add the polynomials. 38. (7x29x+2)+(6x24)In the following exercises, add the polynomials. 39. (5a2+8)+(a24a9)In the following exercises, add the polynomials. 40. (p26p18)+(2p2+11)In the following exercises, subtract the polynomials. 41. (4m26m3)(2m2+m7)In the following exercises, subtract the polynomials. 42. (3b24b+1)(5b2b2)In the following exercises, subtract the polynomials. 43. (a2+8a+5)(a23a+2)In the following exercises, subtract the polynomials. 44. (b27b+5)(b22b+9)

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