Answer
One solution
The solution of the system is $(2,0)$.
Work Step by Step
We are given
$3x+y=6$
$\rightarrow y=-3x+6$
The slope is $-3$. The y-intercept is $6$.
$2x-y=4$
$\rightarrow y=2x-4$
The slope is $2$. The y-intercept is $-4$.
The lines have different slopes. The equations are consistent and independent. Therefore, the system has only one solution.
The lines appear to intersect at $(2,0)$. Check to see if $(2,0)$ makes both equations true.
$0=-3(2)+6$
$0=0$
$y=2x-4$
$0=2(2)-4$
$0=0$
The solution of the system is $(2,0)$.
