Find the solution to the system x+y=10 x^2+y^2=25

Answer 1

x+y=10 => x=10-y

x^2+y^2=25 => (10-y)^2+y^2=25

100-20y+y^2+y^2=25

2y^2+100-20y=25 now use the quadratique formulala to find y and then plug your answer to get x

Answer 2

y = 10-x

x^2 + (10-x)^2 = 25

x^2 + 100 - 20x + x^2 = 25

2x^2 - 20x + 75 = 0

x = [20 +or- sqrt( 400 - 4 *2*75)] / 4

x = [20 +or- sqrt(-200))/4

= [ 20 +or- 10*i*sqrt(2)]/4

= [ 10 +or- 5 i* sqrt(2)]/2

= 5 +or- (5/2) i sqrt(2)