Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 818: 49


The solution of the system of equations is $\left( x,y \right)=\left( \frac{1}{a},3 \right)$.

Work Step by Step

Let us consider the equations (I) and (II) as follows: $\begin{align} & 5ax+4y=17 \\ & ax+7y=22 \end{align}$ And multiply equation (I) by 7 to obtain equation (III): $35ax+28y=119$ Then, multiply equation (II) by to obtain equation (IV): $-4ax-28y=-88$ And add equations (III) and (IV): $\begin{align} & 35ax+28y-4ax-28y=119-88 \\ & 31ax=31 \\ & x=\frac{1}{a} \end{align}$ Substitute the value of x in equation (II) $\begin{align} & 1+7y=22 \\ & 7y=21 \\ & y=3 \end{align}$
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