Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 46

Solve the system
$
\begin{equation}
\begin{aligned}

x-5y =& 6
\\
2x-7y =& 9

\end{aligned}
\end{equation}
$

by substitution.



$
\begin{equation}
\begin{aligned}

x-5y =& 6
&& \text{Solve equation 1 for $x$}
\\
x=& 5y+6
&&
\\
2x-7y =& 9
&& \text{Substitute $5y+6$ for $x$ in equation 2}
\\
2(5y+6) -7y =& 9
&&
\\
10y+12-7y =& 9
&&
\\
3y =& 9-12
&&
\\
3y =& -3
&&
\\
y =& -1
&&

\end{aligned}
\end{equation}
$


Substitute value of $y$ in equation 1




$
\begin{equation}
\begin{aligned}

x =& 5(-1)+6
\\
x =& -5+6
\\
x =& 1

\end{aligned}
\end{equation}
$



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