Answer
The solution of the system is $(3,2)$.
Work Step by Step
Graph both equations in the same coordinate plane.
$y = \frac{1}{3}x+1 \rightarrow $ The slope is $\frac{1}{3}$. The y-intercept is $1$.
$y =-3x+11 \rightarrow $ The slope is $-3$. The y-intercept is $11$.
Find the point of intersection. The lines appear to intersect at $(3,2)$. Check to see if $(3,2)$ makes both equations true.
$y=\frac{1}{3}x+1 \rightarrow 2=\frac{1}{3}(3)+1 \rightarrow 2=2$
$y=-3x+11 \rightarrow 2=-3(3)+11 \rightarrow 2=2 $
The solution of the system is $(3,2)$.
