Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 6

Solve the system $\begin{equation} \begin{aligned} & 9x - y = -4 \\ & y = x + 4 \end{aligned} \end{equation}$ by the substitution method. If a system is inconsistent or has dependent equations, say so.


$\begin{equation} \begin{aligned} 9x - y =& -4 && \text{Given equation} \\ 9x - (x + 4) =& -4 && \text{Substitute $y = x + 4$ in Equation 1} \\ 9x - x - 4 =& -4 && \text{Distributive Property} \\ 8x - 4 =& -4 && \text{Combine like terms} \\ 8x =& 0 && \text{Add each side by $4$} \\ x =& 0 && \text{Divide each side by $8$} \end{aligned} \end{equation}$



$\begin{equation} \begin{aligned} y =& 0 + 4 && \text{Substitute $x = 0$ in Equation 2} \\ y =& 4 && \text{Add} \end{aligned} \end{equation}$


The solution set to the system is $\{ (0,4) \}$.