Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 14

Solve by addition method: $\begin{equation} \begin{aligned} 6x+4y =& -3 \\ 12x-10y =& -15 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} -2(6x+4y) =& (-3)(-2) && \text{Eliminate $x$: Multiply each side of equation 1 by -2} \\ \\ 12x-10y =& -15 && \\ \\ -12x-8y =& 6 && \\ \\ 12x-10y =& -15 && \\ \\ \hline \\ \\ -18y =& -9 && \text{Add the equations} \\ \\ y =& \frac{-9}{-18} && \text{Solve for } y \\ \\ y =& \frac{1}{2} && \end{aligned} \end{equation}$



$\begin{equation} \begin{aligned} 6x + 4 \left( \frac{1}{2} \right) =& -3 && \text{Substitute the value of $y$ in equation 1} \\ \\ 6x + 2 =& -3 && \text{Solve for } x \\ \\ 6x =& -5 && \\ \\ x =& \frac{-5}{6} && \end{aligned} \end{equation}$



The solution is $\displaystyle \left( \frac{-5}{6}, \frac{1}{2} \right)$.