Solve each system by the addition method x2 y2 13 x2 y2

Solve each system by the addition method. {x^2 + y^2 = 13 x^2 - y^2 = 5 {4x^2 - y^2 = 4 4x^2 + y^2 = 4 {x^2 - 4y^2 = -7 3x^2 + y^2 = 31 {3x^2 - 2y^2 = -5 2x^2 - y^2 = -2 {3x^2 + 4y^2 - 16 = 0 2x^2 - 3y^2 - 5 = 0 {16x^2 - 4y^2 - 72 = 0 x^2 - y^2 - 3 = 0 {x^2 + y^2 = 25 (x - 8)^2 + y^2 = 41 {x^2 + y^2 = 5 x^2 + (y - 8)^2 = 41 {y^2 - x = 4 x^2 + y^2 = 4 {x^2 - 2y = 8 x^2 + y^2 = 16

Solution

y^2 - x=4

x^2 + y^2 =4

Subtracting both equations, we get

x²+x=0

x(x+1)=0

x=0 ,-1

at x=0 , y=2 ,-2

and at x=-1 , y=-sqrt3 ,sqrt 3

(0,2),(0,-2),(-1,sqrt3),(-1,-sqrt 3)