Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 32

Solve the system
$\begin{equation} \begin{aligned} x-7y =& 4 \\ -3x+2y =& 6 \end{aligned} \end{equation}$

by substitution.



$\begin{equation} \begin{aligned} x-7y =& 4 && \text{Solve equation 1 for } x \\ x =& 7y + 4 && \\ -3x+2y =& 6 && \text{Substitute $7y+4$ for $x$ in equation 2} \\ -3(7y+4)+2y =& 6 && \\ -21y -12 + 2y =& 6 && \\ -19y =& 6+12 && \\ -19y =& 18 && \\ y =& \frac{-18}{19} && \end{aligned} \end{equation}$


Substitute value of $y$ in equation 1


$\begin{equation} \begin{aligned} x =& 7 \left( \frac{-18}{19} \right)+4 \\ \\ x =& \frac{-126}{19} +4 \\ \\ x =& \frac{-50}{19} \end{aligned} \end{equation}$


The solution is $\displaystyle \left( \frac{-50}{19}, \frac{-18}{19} \right)$.