To find the solution, you can either plug in the points into each equation, or you can do this:
y = 2x - 2
y = -x + 4
Set the two equations equal to each other
2x - 2 = -x + 4 Add 2 on both sides
2x = -x + 6 Add x on both sides
3x = 6 Divide 3 on both sides
x = 2
Now that you know x, you can plug in 2 for x in either of the equations to find y:
y = -x + 4
y = -2 + 4
y = 2
(2,2)
[when you plug (2,2) into each equation]
y = 2x - 2
2 = 2(2) - 2
2 = 4 - 2
2 = 2
y = -x + 4
2 = -2 + 4
2 = 2
