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 $(-2,1)$.