Elementary Algebra
17th Edition
ISBN: 9780998625713
Author: Lynn Marecek, MaryAnne Anthony-Smith
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 2.1, Problem 2.13TI
Solve:
Expert Solution & Answer
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 2 Solutions
Elementary Algebra
Ch. 2.1 - Is y=43 a solution of 9y+2=6y+3 ?Ch. 2.1 - Is y=75 a solution of 5y+3=10y4 ?Ch. 2.1 - Solve: x+19=27 .Ch. 2.1 - Solve: x+16=34 .Ch. 2.1 - Solve: n61=75 .Ch. 2.1 - Solve: p41=73 .Ch. 2.1 - Solve: p23=56 .Ch. 2.1 - Solve: q12=56 .Ch. 2.1 - Solve: b0.47=2.1 .Ch. 2.1 - Solve: c0.93=4.6 .
Ch. 2.1 - Solve: 8y47y7=4 .Ch. 2.1 - Solve: 6z+55z4=3 .Ch. 2.1 - Solve: 5(p3)4p=10 .Ch. 2.1 - Solve: 4(q+2)3q=8 .Ch. 2.1 - Solve: 4(2h3)7h=6(h2)6(h1) .Ch. 2.1 - Solve: 2(5x+2)9x=3(x2)3(x4) .Ch. 2.1 - Translate and solve: Ten more than x is equal to...Ch. 2.1 - Translate and solve: Twelve less than x is equal...Ch. 2.1 - Translate and solve: The difference of 4x and 3x...Ch. 2.1 - Translate and solve: The difference of 7a and 6a...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - Translate into an algebraic equation and solve:...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, determine whether the...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - In the following exercises, solve each equation...Ch. 2.1 - 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How do...Ch. 2.1 - What is the first step in your solution to the...Ch. 2.2 - Solve: 3y=41 .Ch. 2.2 - Solve: 4z=55 .Ch. 2.2 - Solve: a7=42 .Ch. 2.2 - Solve: b6=24 .Ch. 2.2 - Solve: k=8 .Ch. 2.2 - Solve: g=3 .Ch. 2.2 - Solve: 25n=14 .Ch. 2.2 - Solve: 56y=15 .Ch. 2.2 - Solve: 925=45z .Ch. 2.2 - Solve: 56=83r .Ch. 2.2 - Solve: 1827=15c9c3c .Ch. 2.2 - Solve: 1822=12xx4x .Ch. 2.2 - Solve: 4(q2)8=24 .Ch. 2.2 - Solve: 6(r2)12=30 .Ch. 2.2 - Translate and solve: The number 132 is the product...Ch. 2.2 - Translate and solve: The number 117 is the product...Ch. 2.2 - Translate and solve: n divided by 7 is equal to 21...Ch. 2.2 - Translate and solve: n divided by 8 is equal to 56...Ch. 2.2 - Translate and solve: The quotient of q and 8 is...Ch. 2.2 - Translate and solve: The quotient of p and 9 is...Ch. 2.2 - Translate and solve: Two-fifths of f is 16.Ch. 2.2 - Translate and solve: Three-fourths of f is 21.Ch. 2.2 - Translate and solve: The sum of five-eighths and x...Ch. 2.2 - Translate and solve: The sum of three-fourths and...Ch. 2.2 - Translate and solve: Arianna bought a 24-pack of...Ch. 2.2 - Translate and solve: At JB’s Bowling Alley, 6...Ch. 2.2 - Translate and solve: The annual property tax on...Ch. 2.2 - Translate and solve: Stella planted 14 flats of...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - In the following exercises, solve each equation...Ch. 2.2 - 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Solve: 3p14=5p .Ch. 2.3 - Solve: 8m+9=5m .Ch. 2.3 - Solve: 12j=4j+32 .Ch. 2.3 - Solve: 8h=4h+12 .Ch. 2.3 - Solve: 12x+8=6x+2 .Ch. 2.3 - Solve: 9y+4=7y+12 .Ch. 2.3 - Solve: 8q5=4q+7 .Ch. 2.3 - Solve: 7n3=n+3 .Ch. 2.3 - Solve: 2a2=6a+18 .Ch. 2.3 - Solve: 4k1=7k+17 .Ch. 2.3 - Solve: 78x12=18x2 .Ch. 2.3 - Solve: 76y+11=16y+8 .Ch. 2.3 - Solve: 2.8x+12=1.4x9 .Ch. 2.3 - Solve: 3.6y+8=1.2y4 .Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - In the following exercises, solve the following...Ch. 2.3 - 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How...Ch. 2.4 - Solve: 5(x+3)=35 .Ch. 2.4 - Solve: 6(y4)=18 .Ch. 2.4 - Solve: (y+8)=2 .Ch. 2.4 - Solve: (z+4)=12 .Ch. 2.4 - Solve: 2(m4)+3=1 .Ch. 2.4 - Solve: 7(n3)8=15 .Ch. 2.4 - Solve: 13(6u+3)=7u .Ch. 2.4 - Solve: 23(9x12)=8+2x .Ch. 2.4 - Solve: 123(4j+3)=17 .Ch. 2.4 - Solve: 68(k2)=10 .Ch. 2.4 - Solve: 6(p3)7=5(4p+3)12 .Ch. 2.4 - Solve: 8(q+1)5=3(2q4)1 .Ch. 2.4 - Solve: 6[42(7y1)]=8(138y) .Ch. 2.4 - Solve: 12[15(4z1)]=3(24+11z) .Ch. 2.4 - Solve: 0.55(100n+8)=0.6(85n+14) .Ch. 2.4 - Solve: 0.15(40m120)=0.5(60m+12) .Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - Classify the equation as a conditional equation,...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - In the following exercises, solve each linear...Ch. 2.4 - 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Solve the...Ch. 2.6 - Converting temperature While on a tour in Greece,...Ch. 2.6 - Converting temperature Yon was visiting the United...Ch. 2.6 - Solve the equation 2x+3y=6 for y (a) when x=3 (b)...Ch. 2.6 - Solve the equation 5x2y=10 for x (a) when y=10 (b)...Ch. 2.7 - Graph on the number line: (a) x1 (b) x2 (c) x3Ch. 2.7 - Graph on the number line: (a) x2 (b) x3 (c) x1Ch. 2.7 - Graph on the number line and write in interval...Ch. 2.7 - Graph on the number line and write in interval...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve each inequality, graph the solution on the...Ch. 2.7 - Solve each inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality, graph the solution on the...Ch. 2.7 - Solve the inequality 3q7q23 , graph the solution...Ch. 2.7 - Solve the inequality 6x10x+19 , graph the solution...Ch. 2.7 - Solve the inequality 9y+2(y+6)5y24 , graph the...Ch. 2.7 - Solve the inequality 6u+8(u1)10u+32 , graph the...Ch. 2.7 - Solve the inequality 4b3(3b)5(b6)+2b , graph the...Ch. 2.7 - Solve the inequality 9h7(2h)8(h+11)+8h , graph the...Ch. 2.7 - Solve the inequality 14x112x16x+78 , graph the...Ch. 2.7 - Solve the inequality 25z13z115z35 , graph the...Ch. 2.7 - Translate and solve. 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- Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forwardConsider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forward
- Question 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forwardAssume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forward
- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forward
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