Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 32

Solve by substitution: $
\begin{equation}
\begin{aligned}

7x+3y =& -16 \\
x-2y =& 5

\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}

x-2y =& 5
&& \text{Solve equation 2 for } x
\\
x =& 2y + 5
&&
\\
\\
7x+3y =& -16
&& \text{Substitute $2y+5$ for $x$ in equation 1}
\\
7(2y+5) + 3y =& -16
&&
\\
14y + 35 + 3y =& -16
&&
\\
17y =& -51
&&
\\
y =& -3
&&

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x =& 2(-3)+5
\qquad \text{Substitute the value of $y$ in equation 2}
\\
x =& -6+5
\\
x =& -1

\end{aligned}
\end{equation}
$


The solution is $(-1,-3)$.