## Algebra 1: Common Core (15th Edition)

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.