Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6: 38

Answer

$( 4, -10)$

Work Step by Step

First, we simplify the two equations: Equation one: $ 2x -2 -3y -6 =30 \\ 2x -3y =38$ Equation two: $ 3x +6 +2y -2 = -4 \\ 3x +2y = -8$ In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by 3, and we multiply the bottom equation by -2. Then, we add the two equations to obtain: $ -9y -4y = 130 \\-13y = 130 \\ y =-10$ We plug in the given value into the top equation and solve for the other variable: $ 2x - 3(-10) = 38 \\ 2x = 8 \\ x =4$
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