Answer
Intersect at the graph for $(x,y) =(6,2)$, so $y=x-4$ and $y=\dfrac{12-x}{3}$.
Work Step by Step
To solve the given problem we will have to plug the simplest equation into the other equation and then solve for the other variable.
As we are given that $x-y=4$ and $x+3y=12$
This gives $x=4$
Now, $x+3y=12$
or, $4+3y=12$
or, $y=2$
Hence, both the equations gives solution and intersect at the graph for $(x,y) =(6,2)$, so $y=x-4$ and $y=\dfrac{12-x}{3}$