The solution is when they intersect. So to find the answer, set each equation equal to each and solve:
-2x + 3 = x^2 -6x + 3
3 = x^2 -4x + 3
0 = x^2 -4x
0 = x(x-4)
So the solutions are x = 0 and x = 4
Plug in these values into the easier equation to solve for the y's
x = 0 into -2x + 3 gives y = 3
So one solution is (0, 3)
x = 4 into -2x + 3 gives y = -5
So the second solution is (4, -5)