Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 32

Solve by substitution: $\begin{equation} \begin{aligned} 7x+3y =& -16 \\ x-2y =& 5 \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} x-2y =& 5 && \text{Solve equation 2 for } x \\ x =& 2y + 5 && \\ \\ 7x+3y =& -16 && \text{Substitute $2y+5$ for $x$ in equation 1} \\ 7(2y+5) + 3y =& -16 && \\ 14y + 35 + 3y =& -16 && \\ 17y =& -51 && \\ y =& -3 && \end{aligned} \end{equation}$



$\begin{equation} \begin{aligned} x =& 2(-3)+5 \qquad \text{Substitute the value of $y$ in equation 2} \\ x =& -6+5 \\ x =& -1 \end{aligned} \end{equation}$


The solution is $(-1,-3)$.