Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 10

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

6x + 5y =& 4 \\
-4x + 2y =& 8

\end{aligned}
\end{equation}
$ by the elimination method. If a system is inconsistent or has dependent equations, say so.


$
\begin{equation}
\begin{aligned}

6x + 5y =& 4
&&
\\
-6x + 3y =& 12
&& \frac{3}{2} \times \text{ Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{6x+} 8y =& 16
&& \text{Add}
\\
y =& 2
&& \text{Divide each side by $8$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

6x + 5(2) =& 4
&& \text{Substitute $y = 2$ in Equation 1}
\\
6x + 10 =& 4
&& \text{Multiply}
\\
6x =& -6
&& \text{Subtract each side by $10$}
\\
x =& -1
&& \text{Divide each side by $6$}


\end{aligned}
\end{equation}
$


The solution set to the system is $\{ (-1,2) \}$.