Question

What are the solutions of the following system?

Answer 1

X^2 + y^2 = 25
2x + y = -5.....y = -2x - 5

x^2 + (-2x - 5)^2 = 25
x^2 + (-2x - 5)(-2x - 5) = 25
x^2 + (4x^2 + 20x + 25) = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x + 4) = 0

5x = 0         2(0) + y = -5
x = 0            y = -5

x + 4 = 0      2(-4) + y = -5
x = -4           -8 + y = -5
                     y = 3

solutions are : x = 0, y = -5.....and x = -4, y = 3