THE LINE Y=X+4 INTERSECTS THE CURVE

2X^2 + 3XY - Y^2 + 1 = 0

1 answer

So it does.

use substitution to solve ...
2x^2 + 3x(x+4) - (x+4)^2 + 1 = 0
2x^2 + 3x^2 + 12x - x^2 - 8x - 16 + 1 = 0
4x^2 + 4x - 15 = 0
(2x-3)(2x+5) = 0

I am sure you can finish it.