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

The solution of the system is $(1,1)$. Thus, the system has one solution.
Graph both equations in the same coordinate plane. $3x -y=2\rightarrow y=3x-2$ The slope is $3$. The y-intercept is $-2$. $4y=-x+5 \rightarrow y=-\frac{1}{4}x+\frac{5}{4}$ The slope is $-\frac{1}{4}$. The y-intercept is $\frac{5}{4}$. Find the point of intersection. The lines appear to intersect at $(1,1)$. Check to see if $(1,1)$ makes both equations true. $y=3x-2 \rightarrow 1=3(1)-2 \rightarrow 1=1$ $y=-\frac{1}{4}x+\frac{5}{4} \rightarrow 1=-\frac{1}{4}(1)+\frac{5}{4} \rightarrow 1=1$ The solution of the system is $(1,1)$. Thus, the system has one solution.