College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 5, Systems of Equations and Inequalities - Section 5.1 - Systems of Linear Equations in Two Variations - 5.1 Exercises - Page 447: 56

Answer

$x=\frac{b}{b-a},y=\frac{-a}{b-a}$

Work Step by Step

We solve the second equation for $x$: $x+y=1$ $x=1-y$ Plugging this into the first equation, we get: $ax+by=0\\a(1-y)+by=0\\a-ay+by=0\\y(b-a)=-a\\y=\frac{-a}{b-a}$ Thus, we have $x=1-\frac{-a}{b-a}=\frac{b}{b-a}$
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