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

Solve by addition method: $\begin{equation} \begin{aligned} 4x-y =& 9 \\ 2x+3y =& -13 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} 3 (4x-y) =& (9)3 && \text{Eliminate $y$: Multiply each side of equation 1 by 3} \\ 2x+3y =& -13 && \\ \\ 12x-3y =& 27 && \\ 2x+3y =& -13 && \\ \hline \\ 14x =& 14 && \text{Add the equations} \\ x =& 1 && \text{Solve for } x \end{aligned} \end{equation}$




$\begin{equation} \begin{aligned} 2(1)+3y =& -13 && \text{Substitute the value of $x$ in equation 2} \\ 2+3y =& -13 && \text{Solve for } y \\ 3y =& -15 && \\ y =& -5 && \end{aligned} \end{equation}$


The solution is $(1,-5)$.