Algebra: A Combined Approach (4th Edition)

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

Chapter 4 - Review - Page 328: 29


$$x=22$$ $$y=-6$$

Work Step by Step

Let $x$ be the larger number and $y$ be the smaller number. Equation 1: $x\:+\:y = 16$ Equation 2: $3x-y=72$ We can solve for the numbers using the addition method. Adding equations & 2: $$x\:+\:y = 16$$ $$+$$ $$3x-y=72$$ $$=$$ $$4x=88$$ Divide both sides by $4$: $$\frac{4x}{4}=\frac{88}{4}$$ $$x=22$$ Substitute this value of $x$ to equation 1: $$x\:+\:y = 16$$ $$22+y=16$$ Subtract $22$ from both sides: $$22-22+y=16-22$$ $$y=-6$$ Use equation 2 to check: $$3x-y=72$$ $$3(22)-(-6)=72$$ $$66+6=72$$ $$72=72$$
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