Question

What is the solution set of this system of equations?

y = x2 − 3x − 4
x = y + 8

{(-1, 0), (4, 0)}
{(8, 0), (0, 8)}
{(0, 0)}
{(2, -6)}
There is no real solution

Answer 1

\[y = x^2 − 3x − 4\]
\[x = y + 8\]
\[x = x^2 − 3x − 4 + 8\]
\[x^2 − 4x +4=0\]
\[(x-2)(x-2)=0\]
\[x=2 , y=x-8=2-8=-6\]

\[y=-6\]