Answer
The system has only one solution.
Work Step by Step
We are given
$3x+2y=1 $
$\rightarrow 2y=-3x+1$
$ \rightarrow y=\frac{-3}{2}x+\frac{1}{2}$
The slope is $\frac{-3}{2}$.
$4y=6x+2$
$ \rightarrow y=\frac{3}{2}x+\frac{1}{2}$
The slope is $\frac{3}{2}$.
The lines intersect at one point. The lines have different slopes. The equations are consistent and independent. Therefore, the system has only one solution.
