x^2 - y = 1
2x^2 + 3y = 17
multiply the top equation by -3
-3x^2 + 3y = -3
2x^2 + 3y = 17
add 3x^2 to both sides in the top equation and subtract 2x^2 from both sides in the bottom equation
3y = -3 + 3x^2
3y = 17 - 2x^2
see how the left side of both equations is 3y? the same? that means the right sides are the same too, so we can do this:
-3 + 3x^2 = 17 - 2x^2
-3 + 5x^2 = 17
5x^2 = 20
x^2 = 4
x = -2 or +2
x^2 - y = 1
4 - y = 1
-y = -3
y = 3
Answer: x = -2 or +2, y = 3