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: 36

Answer

(-3,-6)

Work Step by Step

First, we simplify the two equations: Equation one: $ -2x -4 +4y -12 = -34 \\ -2x + 4y = -18 $ Equation two: $ 3x + 12 - 5y -10 = 23 \\ 3x - 5y = 21 $ 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: $ 12y - 10y = -12 \\ 2y = -12 \\ y =- 6 $ We plug in the given value into the top equation and solve for the other variable: $ -2x +4(-6) = -18 \\ -2x = 6 \\ x = -3$
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