Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 34

Solve by addition method: $\begin{equation} \begin{aligned} 6x+y =& 12 \\ 9x+2y =& 18 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} -2(6x+y) =& (12)(-2) && \text{Eliminate $y$: Multiply each side of equation 1 by -2} \\ 9x + 2y =& 18 && \\ -12x-2y =& -24 && \\ 9x + 2y =& 18 && \\ \hline \\ -3x =& -6 && \text{Add the equations} \\ x =& 2 && \text{Solve for } x \end{aligned} \end{equation}$


Substitute the value of $x$ in equation 1


$\begin{equation} \begin{aligned} 6(2)+y =& 12 \\ 12+y =& 12 \qquad \text{Solve for } y \\ y =& 0 \end{aligned} \end{equation}$


The solution is $(2,0)$.