Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 8

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

5x + y =& 12 \\
2x - 2y =& 0

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


$
\begin{equation}
\begin{aligned}

10x + 2y =& 24
&& 2 \times \text{ Equation 1}
\\
2x - 2y =& 0
&&
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

12x \phantom{-2y} =& 24
&& \text{Add}
\\
x =& 2
&& \text{Divide each side by $12$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

5(2) + y =& 12
&& \text{Substitute $x = 2$ in Equation 1}
\\
10 + y =& 12
&& \text{Multiply}
\\
y =& 2
&& \text{Subtract each side by $10$}

\end{aligned}
\end{equation}
$


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