Solve the following system for all solutions:

(x - 1)^2 + (y + 3)^2 = 13

x + y = -3

( -4, -1 ) and ( -9, - 6)

Step-by-step explanation:

Given(x - 1)^2 + (y + 3)^2 = 13 x + y = -3Solution

From the second equation we get

x = - y - 3

Substituting x in the first equation

(- y - 3 - 1)^2 + (y + 3)^2 = 13(-y - 4)^2 + (y + 3)^2 = 13(y+4)^2 + (y+3)^2 = 13y^2 + 8y + 16 + y^2 + 6y + 9 = 132y^2 + 14y + 12 = 0y^2 +7y +6 = 0(y+1)(y+6) = 0y = - 1y = - 6

Then

x = -4x = - 9

Answer

( -4, -1 ) and ( -9, - 6)