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