Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 56

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

-x+6y =& 8 \\
2x+5y =& 1

\end{aligned}
\end{equation}
$

by substitution.



$
\begin{equation}
\begin{aligned}

-x+6y =& 8
&& \text{Solve equation 1 for } x
\\
-x =& 8-6y
&&
\\
x =& 6y-8
&&
\\
2x +5y =& 1
&& \text{Substitute $6y-8$ for $x$ in equation 2}
\\
2(6y-8)+5y =& 1
&&
\\
12y-16 +5y =& 1
&&
\\
17y =& 1+16
&&
\\
17y =& 17
&&
\\
y =& 1
&&

\end{aligned}
\end{equation}
$


Substitute value of $y$ in equation 1




$
\begin{equation}
\begin{aligned}

x =& 6(1)-8 \\
x =& 6-8 \\
x =& -2

\end{aligned}
\end{equation}
$



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