Solve the following system x^2+y^2=25, 2x+y=10

Hello:

x²+y²=25 ... (1)

, 2x+y=10 ... (2)

by (2) : y = 10 - 2x

subsct in (1):

x² + (10-2x) ² = 25

x² + 100 - 20x + 4x² = 25

5x²-20x + 75 = 0

x² - 4x + 15 = 0

(x+3) (x-5) = 0

x+3 = 0 or x-5 = 0

x = - 3 or x = 5

if x = - 3 y = 10 - 2 (-3) = 16

if x = 5 y = 10-2 (5) = 0

two solutions : (-3, 16), (5, 0)