Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 12

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

& -3x + y = 6 \\
& y = 6 + 3x

\end{aligned}
\end{equation}
$ by the elimination method. If a system is inconsistent or has dependent equations, say so.


$
\begin{equation}
\begin{aligned}

-3x + y =& 6
&&
\\
-3x + y =& 6
&& \text{Rewrite Equation 2}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-3x + y =& 6
&&
\\
3x - y =& -6
&& -1 \times \text{ Equation 2}
\\
\hline
\\
0 =& 0
&&

\end{aligned}
\end{equation}
$



Adding the two equations give a true statement $0 = 0$. This means that the system is dependent and i thas infinitely many solutions. The solution set to the system is $\{ (x,y) | -3x + y = 6 \}$.