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 $(2,0)$.