Hi there!
We can rewrite the system of equations into one equation.
[tex] {x}^{2} + 16x + 32 = - {x}^{2} + 2[/tex]
Now bring all terms to the left.
[tex]2 {x}^{2} + 16x + 30 = 0[/tex]
Divide by 2.
[tex] {x}^{2} + 8x + 15 = 0[/tex]
[tex](x + 3)(x + 5) = 0[/tex]
AB = 0, so A = 0 or B = 0
[tex]x + 3 = 0 \: \: \: or \ \: \: x + 5 = 0[/tex]
Subtract either 3 or 5.
[tex]x = - 3 \: \: \: \: \: \: or \: \: \: x = - 5[/tex]
x = -3 gives:
[tex]y = - {( - 3)}^{2} + 2 = - 9 + 2 = - 7[/tex]
x = -5 gives:
[tex]y = - {( - 5)}^{2} + 2 = - 25 + 2 = - 23[/tex]
