Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - Mid-Chapter Quiz - Page 393: 6


$x = -15$ $y = -22$

Work Step by Step

To solve a system of equations using substitution, we plug in an expression in place of a variable. In this system of equations, $x$ is expressed in terms of $y$ in one equation. We can use this equation to substitute for $x$ in the other equation: $y - 8 = 2(y + 7)$ Use the distributive property on the left side of the equation: $y - 8 = 2y + 14$ Add $8$ to each side of the equation to move constants to the right side of the equation: $y = 2y + 22$ Subtract $2y$ from each side of the equation to move variables to the left side of the equation: $-y = 22$ Divide each side of the equation by $-1$ to solve for $x$: $y = -22$ Now that we have the value for $y$, we can substitute it into one of the equations to solve for $x$: $x = -22 + 7$ Multiply first: $x = -15$
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