Answer
$\{(-2,4), (1,1)\}$
Work Step by Step
We are given two systems of equations: $x^2-y=0 ~~~~(1) \\ x+y=2 ~~~~(2)$
Equation (2) can be re-written as: $y=2-x$
Equation -(1) becomes: $x^2 -2+x=0 \implies (x+2)(x-1) =0$
Apply zero factor property $x+2 =0 \implies x=-2$ and $x-1=0 \implies x=1$
Plug the values of $x$ into the second equation to calculate the values of $y$.
$-2 +y=2 \implies y=4$
and $1+y=2 \implies y=1$
Therefore, the required solution set is: $\{(-2,4), (1,1)\}$
