use substitution method to solve y = x^2 , y = x - 12

Question

pls solve for me the question that i asked above, am having difficulty substituting it.

thanks.

Answer 1

Substitute y=x^2 in the second equation:
x^2=x-12. This becomes the quadratic: x^2-x+12=0.
This equation has no real roots, but if the second equation had been y=x+12, we would have: x^2-x-12=0 which factorises: (x-4)(x+3) so x=4 and -3, from which y=16 and 9.
Back to x^2-x+12=0. The complex roots are x=(1±i*sqrt(47))/2.
From this we have complex values for y: y=(1±2i*sqrt(47)-47)/4=(-46±2i*sqrt(47))/4.