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: 47


The solution of the system of equations is $\left( x,y \right)=\left( 6,-1 \right)$.

Work Step by Step

We have to simplify the system of equations: The first equation: $\begin{align} & \frac{x+2}{2}-\frac{y+4}{3}=3 \\ & 3x+6-2y-8=18 \end{align}$ $3x-2y=20$ And second equation: $\begin{align} & \frac{x+y}{5}=\frac{x-y}{2}-\frac{5}{2} \\ & 2x+2y=5x-5y-25 \end{align}$ $3x-7y=25$ And multiply equation $3x-2y=20$ by −1 to obtain: $-3x+2y=-20$ And add equations $3x-7y=25$ and $-3x+2y=-20$ to obtain: $\begin{align} & 3x-7y-3x+2y=25-20 \\ & -5y=5 \\ & y=-1 \end{align}$ Put the value $y=-1$ in equation $3x-2y=20$ to obtain: $\begin{align} & 3x+2=20 \\ & 3x=18 \\ & x=6 \end{align}$ Thus, the solution set $\left( x,y \right)$ to the system of equations is $\left( 6,-1 \right)$.
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