Question

Solve the following system for all solutions:

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

x + y = -3​

Answer 1

• ( -4, -1 ) and ( -9, - 6)

Explanation:

Given

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

Solution

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

Then

• x = -4
• x = - 9

Answer

• ( -4, -1 ) and ( -9, - 6)