Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 6

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

4x-y =& 9 \\
2x+3y =& -13

\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}

3 (4x-y) =& (9)3
&& \text{Eliminate $y$: Multiply each side of equation 1 by 3}
\\
2x+3y =& -13
&&
\\
\\
12x-3y =& 27
&&
\\
2x+3y =& -13
&&
\\
\hline
\\
14x =& 14
&& \text{Add the equations}
\\
x =& 1
&& \text{Solve for } x

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

2(1)+3y =& -13
&& \text{Substitute the value of $x$ in equation 2}
\\
2+3y =& -13
&& \text{Solve for } y
\\
3y =& -15
&&
\\
y =& -5
&&

\end{aligned}
\end{equation}
$


The solution is $(1,-5)$.