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: 44



Work Step by Step

First, we simplify the two equations: Equation one: $\frac{3x-3y-8x + 4y}{12} = -1/4 \\ -5x +y =-3 $ Equation two: $ \frac{4x + 2y +3x +3y}{6} = \frac{17}{6} \\7x +5y = 17 $ 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 -5, and we multiply the bottom equation by 1. Then, we add the two equations to obtain: $ 25x + 7x = 32 \\ 32x =32 \\ x=1 $ We plug in the given value into the top equation and solve for the other variable: $ -5(1) +y=-3\\ y=2$
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