Chapter 10 - Section 10.8 - Systems of Nonlinear Equations - 10.8 Exercises - Page 754: 21

$(-2, -2)$

Given the system of equations: 1. $x - 2y = 2$ 2. $y^2 - x^2 = 2x + 4$ It asks to find all solutions. Substitute $x = 2y + 2$ $y^2 - (2y+2)^2 = 2(2y+2) + 4$ $y^2 - 4y^2 - 8y - 4 = 4y + 4 + 4$ $-3y^2 - 12y - 12 = 0$ $-3(y^2 + 4y + 4) = 0$ $-3 ((y+2)^2) = 0$ $y = -2$ Substitute the values into the equation $x = 2(-2) + 2$ $x = -2$ All solutions: $(-2, -2)$