Answer
The system has an infinite number of solutions.
Solution set = $\{(x,y)\ |\ 2x+3y=6\}$
Work Step by Step
Graph each line
(plot two points per line, such as the interceptcs)
$2x+3y=6:\quad \left[\begin{array}{lll}
x=0 & ... & y=0\\
0+3y=6 & & 2x+0=6\\
y=2 & & x=3\\
(0,2) & & (3,0)
\end{array}\right]$
$4x+6y=12:\quad \left[\begin{array}{lll}
x=0 & ... & y=0\\
0+6y=12 & & 4x+0=12\\
y=2 & & x=3\\
(0,2) & & (3,0)
\end{array}\right]$
The lines coincide.
The system has an infinite number of solutions.
Solution set = $\{(x,y)\ |\ 2x+3y=6\}$
