Beginning Algebra With Applications, Chapter 6, Cumulative Exercises, Section Cumulative Exercises, Problem 22

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

2x-3y =& -7
\\
x+4y =& 2

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x+4y =& 2
&& \text{Solve equation 2 for } x
\\
x =& 2-4y
&&
\\
2x-3y =& -7
&& \text{Substitute $2-4y$ for $x$ in equation 1}
\\
2(2-4y)-3y =& -7
&& \text{Solve for } y
\\
4-8y-3y =& -7
&&
\\
-11y =& -11
&&
\\
y =& 1
&&

\end{aligned}
\end{equation}
$


Substitute the value of $y$ in equation 2


$
\begin{equation}
\begin{aligned}

x =& 2-4 (1) \qquad \text{Solve for } x
\\
x =& 2-4
\\
x =& -2

\end{aligned}
\end{equation}
$


The solution is $(-2,1)$.