Solve each system of equations

X^2+y^2+18x+29=0

X+y=1

two solutions : (-3; 4) and (-5; 6)

Step-by-step explanation:

hello:

X²+y²+18x+29=0 ... (1)

X+y=1 ... (2)

by (2) : y = 1 - x

put this value in (1) : x² + (1-x) ² + 18x+29 = 0

x² + 1 + x² - 2x+18x + 29 = 0

2x²+16x + 30 = 0

x²+8x+15 = 0

delta = b²-4ac a=1 b=8 c = 15

delta = (8) ²-4 (1) (15) = 64-60 = 4 = 2²

X1 = (-8+2) / 2 = - 3

X2 = (-8-2) / 2 = - 5

case 1 : x = - 3 y = 1 - (-3) = 4

case 2 : x = - 5 y = 1 - (-5) = 6