#### Answer

The solution of the system is $(1,1)$.
Thus, the system has one solution.

#### Work Step by Step

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.