How do you solve x^2-y^2=xy-1 to find out the values of x & y?

Answer 1

0 = y^2 + xy - x^2 - 1

Quadratic in terms of y.

Quadratic formula says:

y =[ -x +or- sqrt ( x^2 - 4(1)(-x^2-1))]/2

= [ -x +or- sqrt( x^2 + 4x^2 + 4)]/2

= [ -x +or- sqrt( 5x^2 + 4)]/2

Answer 2

Typically, you want y as a function of x.

y^2 + xy - x^2-1 = 0

Using the quadratic formula with A=1 , B = x, C = -x^2-1

y = [-x +or- sqrt ( x^2 - 4(-x^2-1) ] / 2

= [-x +or- sqrt( x^2 + 4x^2 + 4)] / 2

= [ -x +or- sqrt ( 5x^2 + 4)]/2

Now you can graph that function and get your solutions