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 $\{ (2,2) \}$.