Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 20

Solve the system $\begin{equation}
\begin{aligned}

& 2x - y = 6 \\
& y = 5x

\end{aligned}
\end{equation}
$ by substitution. If the system is inconsistent or has dependent equations.

Since equation 2 is solved for $y$, we substitute $3x$ for $y$ in equation 1.



$
\begin{equation}
\begin{aligned}

2x - 5x =& 6
&& \text{Substitute $y = 5x $}
\\
-3x =& 6
&& \text{Combine like terms}
\\
x =& -2
&& \text{Divide each side by $-3$}

\end{aligned}
\end{equation}
$


We found $x$. Now we solve for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

y =& 5(-2)
&& \text{Substitute $x = -2$}
\\
y =& -10
&&

\end{aligned}
\end{equation}
$