Algebra: A Combined Approach (4th Edition)

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

Chapter 4 - Review - Page 329: 44

Answer

$$x=16$$ $$y=-4$$

Work Step by Step

Equation 1: $-x - 15y = 44$ Equation 2: $2x + 3y = 20$ Multiply equation 1 by $2$: $$[-x - 15y = 44]\cdot 2$$ $$-2x - 30y = 88$$ Add this equation to equation 2: $$-2x - 30y = 88$$ $$+$$ $$2x + 3y = 20$$ $$=$$ $$-27y=108$$ Divide both sides by $-27$: $$\frac{-27y}{-27}=\frac{108}{-27}$$ $$y=-4$$ Substitute this value of $y$ to equation 1: $$-x - 15y = 44$$ $$-x - 15(-4) = 44$$ $$-x +60 = 44$$ Subtract $60$ from both sides: $$-x +60 -60= 44-60$$ $$-x=-16$$ $$x=16$$ Use equation 2 to check: $$2x + 3y = 20$$ $$2(16) + 3(-4) = 20$$ $$32-12=20$$ $$20=20$$
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