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 $\{ (0,4) \}$.