we have that
y=x²----> equation 1
y=x+2-----> equation 2
multiply equation 1 by -1
-y=-x²
add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation(x²-x)=2
Complete the square. Remember to balance the equation by adding the same constants to each side
(x²-x+0.5²)=2+0.5²
Rewrite as perfect squares(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1
for x=2
y=x²----> y=2²----> y=4
the point is (2,4)
for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)
the answer is
the solution of the system are the points
(2,4) and (-1,1)