Solve the system x 12 y2 25 x y2 4 Enter your solutions

Solve the system: (x - 1)^2 + y^2 = 25 x - y^2 = -4 Enter your solutions as ordered pairs using (, ) and separate each ordered pair with a comma. If there is no solution, enter \"none\".

Solution

( x - 1)^2 + y^2 = 25

x - y^2 = -4

from equation 2

x = y^2 - 4

plugging this value into equation 1

( y^2 - 4 - 1 )^2 + y^2 = 25

y^4 + 25 - 10y^2 + y^2 = 25

y^4 - 9y^2 = 0

y^2 ( y^2 - 9 ) = 0

y = 0

y = + - 3

x = 5 , - 4

solutions are

(-4,0) , (5,3) , (5,-3)