Answer:
Third option: (0,-5) and (-4,3)
Step-by-step explanation:
x^2 + y^2 = 25
2x + y = -5
y = -5 - 2x
x^2 + (-5-2x)^2 = 25
x^2 + 25 + 20x + 4x^2 = 25
5x^2 + 20x + 25 = 25
5x^2 + 20x = 0
5x(x+4) = 0
5x=0 --> x=0
x+4=0 --> x=-4
2(-4) + y = -5
-8 + y = -5
y = 3 --> (-4,3)
2(0) + y = -5
0 + y = -5
y = -5 --> (0,-5)
Therefore, the solutions to the system of equations are (0,-5) and (-4,3)