4X+2Y=10
3X+Y=8
Y= -3X+8

Solve the second equation for Y.

4X+2(-3X+8)=10
4X-6X+16=10
-2X+16=10
-2X= -6
X=3

Substitute the second equation for Y into equation one and solve for X.

3(3)+Y=8
9+Y=8
Y= -1

Substitute the value of X into the revised equation two and solve for Y.

(3,-1)

Then you get your points.