Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Cumulative Review - Page 333: 31

Answer

The solution to the system is the ordered pair $(-\frac{15}{7},-\frac{5}{7})$.

Work Step by Step

Equation 1: $-x-\frac{y}{2}=\frac{5}{2}$ Equation 2: $\frac{x}{6}-\frac{y}{2}=0$ Multiply equation 1 by $-1$: $$[-x-\frac{y}{2}=\frac{5}{2}]\cdot-1$$ $$x+\frac{y}{2}=-\frac{5}{2}$$ Add this equation to equation 2: $$x+\frac{y}{2}=-\frac{5}{2}$$ $$+$$ $$\frac{x}{6}-\frac{y}{2}=0$$ $$=$$ $$\frac{7x}{6}=-\frac{5}{2}$$ Multiply both sides by $6$: $$(\frac{7x}{6})\cdot6=(-\frac{5}{2})\cdot6$$ $$7x=-15$$ Divide both sides by $7$: $$\frac{7x}{7}=\frac{-15}{7}$$ $$x=-\frac{15}{7}$$ Substitute this value of $x$ to equation 1: $$-x-\frac{y}{2}=\frac{5}{2}$$ $$-(-\frac{15}{7})-\frac{y}{2}=\frac{5}{2}$$ $$\frac{15}{7}-\frac{y}{2}=\frac{5}{2}$$ Subtract $\frac{15}{7}$ from both sides: $$\frac{15}{7}-\frac{15}{7}-\frac{y}{2}=\frac{5}{2}-\frac{15}{7}$$ $$-\frac{y}{2}=\frac{5}{2}-\frac{15}{7}$$ Multiply both sides by $14$: $$(-\frac{y}{2})\cdot14=(\frac{5}{2}-\frac{15}{7})\cdot14$$ $$-7y=35-30$$ $$-7y=5$$ Divide both sides by $-7$: $$\frac{-7y}{-7}=\frac{5}{-7}$$ $$y=-\frac{5}{7}$$ Therefore, the solution to the system is the ordered pair $(-\frac{15}{7},-\frac{5}{7})$.
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