Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 4 - Review Exercises - Page 338: 25


$$(2, 4)$$

Work Step by Step

To solve a system of equations by the addition method, you have to transform the equations so that the coefficients of one of the variables differ only in sign. In this problem, we want to work with the $y$ variable. We will transform the first equation because it's easier to work with. We multiply the first equation by $-1$ to get: $$-1(x + y) = -1(6)$$ We simplify to get: $$-x - y = -6$$ We now put the two equations together to add them: $$-x - y = -6$$ $$2x + y = 8$$ We add them to get the following equation: $$x = 2$$ We can now plug in what we got for $x$ into one of the equations to get $y$: $$2 + y = 6$$ Subtract each side by $2$ to solve for $y$: $$y = 4$$ $$(2, 4)$$
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