Answer
(2, 6) and (-1, 3)
Work Step by Step
For this problem,
Equation 1: x - y = -4
Equation 2: $x^{2}$ - y = -2
For substitution we need to solve for a variable. In this problem, we will solve for y in Equation 1 to get Equation 3:
y = x + 4 (Equation 3)
We then substitute that into Equation 2 and solve for x:
$x^{2}$ - (x + 4) = -2
$x^{2}$ - x - 4 = -2
$x^{2}$ - x - 2 = 0
(x - 2)(x + 1) = 0
x = 2 and x = -1
We then use Equation 3:
y = 2 + 4 = 6
y = -1 + 4 = 3
Therefore (2, 6) and (-1, 3) are solutions. Furthermore, the two graphs cross at (2, 6) and (-1, 3), so the answer is confirmed.
