Answer
\[\left\{ \left( x,y \right)|3x-2y=6 \right\}or\left\{ \left( x,y \right)|6x-4y=12 \right\}\]
Work Step by Step
Observing the system, a method of addition becomes appropriate.
Let equation 1 be \[3x-2y=6\] and equation 2 be \[6x-4y=12\]
Multiplying equation 1 by a factor 2,
\[\begin{align}
& 2\left( 3x \right)-2\left( 2y \right)=12 \\
& 6x-4y=12
\end{align}\]
Now, subtract equation 1 by 2, and get
\[0=0\]
Both variables are eliminated and the statement is true. So, the system has infinitely many solutions.
An ordered-pair satisfying one equation satisfies the other.
In set notation, the solution will be \[\left\{ \left( x,y \right)|3x-2y=6 \right\}or\left\{ \left( x,y \right)|6x-4y=12 \right\}\]
