Explanation Given Information: The system of equations is: x − 2 y + z = 1 3 x + y − 2 z = − 22 4 x + z = − 11 Formula used: Steps to solve the system of three Linear Equations in Three Variables Step 1 Write each equation in standard form A x + B y + C z = D Step 2 Choose two equations, and eliminate any one of the variables by using the addition method. Step 3 Choose a different two equations and eliminate the same variable. Step 4 Once steps 2 and 3 are complete, you should have 2 equations in 2 variables. Solve this system by using the substitution or the addition method. Step 5 Substitute the values of the variables found in step 4 into any of the three original equations that contain the third variable. Solve for the third variable. Calculation: Consider the system of equation: x − 2 y + z = 1 …… (1) 3 x + y − 2 z = − 22 …… (2) 4 x + z = − 11 …… (3) Multiplying equation (2) by 2: 6 x + 2 y − 4 z = − 44 …… (4) Adding equation (1) and (4): 7 x − 3 z = − 43 That is: z = 1 3 ( 7 x

Aleks 360 Access Card (18 Weeks) for Beginning & Intermediate Algebra

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ISBN: 9780077564018

Author: ALEKS Corporation

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Chapter 8, Problem 10CRE

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To calculate: The solution of the system of equation x−2y+z=1;3x+y−2z=−22 and 4x+z=−11.

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Chapter 8, Problem 9CRE

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For Exercises 15–22, solve the system by using the addition method. (See Examples 3-4) 15. 2x + 3y = 11 16. 3x + y² = 21 17. x - xy = 20 18. 4xy + 3y² = -9 2 + 4y = 8 4x - 2y = -2 -2x2 + 3xy = -44 2xy + y = -5 21. x = 1- y 9x - 4y? = 36 19. 5x - 2y2 = 1 20. 6x + 5y = 38 7x - 3y = 9 22. 4x = 4 - y? 16y = 144 + 9x? 2x - 3y = -4

An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. Exercises 97–98 involve supply and demand. 97. A chain of electronics stores sells hand-held color televisions. The weekly demand and supply models are given as follows: Number sold Demand model per week N = -5p + 750 Price of television Number supplied to the chain per week N = 2.5p. 1apow hjddns a. How many hand-held color televisions can be sold and supplied at $120 per television? b. Find the price at which supply and demand are equal. At this price, how many televisions can be supplied and sold each week?

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Chapter 8 Solutions

Aleks 360 Access Card (18 Weeks) for Beginning & Intermediate Algebra

Ch. 8.1 - Find the domain and range of the relation. { ( 0 ,...Ch. 8.1 - Prob. 2SP Ch. 8.1 - Prob. 3SP Ch. 8.1 - Prob. 4SP Ch. 8.1 - Prob. 5SP Ch. 8.1 - Prob. 6SP Ch. 8.1 - Prob. 7SP Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...Ch. 8.1 - The linear equation, y = − 0.014 x + 64.5 , for...

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The solution of the system of equation x − 2 y + z = 1 ; 3 x + y − 2 z = − 22 and 4 x + z = − 11 .

Solution Summary: The author explains how to solve the system of three Linear Equations in Three Variables.

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To calculate: The solution of the system of equation x−2y+z=1;3x+y−2z=−22 and 4x+z=−11.

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Chapter 8 Solutions