Question

Where does y=2x-3 and y=-x+3 intersect?

Answer 1

`y=2x-3\\ y=-x+3\\\\ 2x-3=-x+3\\ 3x=6\\ x=2\\\\ y=-2+3\\ y=1\\\\ \text{They intersect at the point }(2,1)`

Answer 2

Substitute -x+3 for the y in the first equation so it reads -x+3=2x-3 then solve for x getting x=2. thats your x coordinate for the point of intersection. Then choose either equation and plug in 2 for x and solve. Thats your y coordinate, which is 1. So the point of intersection is (2,1).