Beginning Algebra With Applications, Chapter 6, Test, Section Test, Problem 22

Solve by addition method:
$
\begin{equation}
\begin{aligned}

9x-2y =& 17 \\
5x+3y =& -7

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

3(9x-2y) =& (17)3
&& \text{Eliminate $y$: Multiply each side of equation 1 by 3 }
\\
2 (5x+3y) =& (-7)2
&& \text{and Multiply each side of equation 2 by 2}
\\
\\
27x - 6y =& 51
&&
\\
10x + 6y =& -14
&&
\\
\hline
\\
37x =& 37
&& \text{Add the equations}
\\
x =& 1
&& \text{Solve for } x

\end{aligned}
\end{equation}
$


Substitute the value of $x$ in equation 1


$
\begin{equation}
\begin{aligned}

9(1)-2y =& 17
\qquad \text{Solve for } y
\\
9-2y =& 17
\\
-2y =& 8
\\
y =& -4

\end{aligned}
\end{equation}
$


The solution is $(1,-4)$.