Solve the following system of equations and show all work. y = x2 + 3 y = x + 5

set the two equations equal to each other
x^2 + 3 = x + 5
x^2 -x - 2 = 0
factor polynomial
(x+1) * (x-2) = 0
therefore, x = -1 or 2
a) x = -1
(-1)^2 + 3 = -1 + 5
1 + 3 = 4
4 = 4
b) x = 2
2^2 + 3 = 2 + 5
4 + 3 = 7
7 = 7