Question

Write a nonlinear system of equations in two variables to model the application problem. Solve the system of equations algebraically. Show your work.

Find two complex numbers, x and y, whose sum is -10 and whose product is 29.

Answer 1

just follow the given info:
x+y=-10
x*y=29

this is your system.
you can express x in term of y or y in a term of x from the first equation & substitute- in second.
Solve it for the variable.

Answer 2

x + y = -10 ...(1)
xy = 29 ...(2)

from (2), x = 29/y
put that into (1): 29/y + y = -10
(29+y²)/y = -10
29+y² = -10y
y² + 10y + 29 = 0\[y = [ -10 \pm \sqrt{100-116} ] / 2\]\[y = [-10\pm2\sqrt{-4}] / 2\]\[y=-5\pm \sqrt{-4}\]\[y=-5\pm2i\]

x + (-5+2i) = -10 and
x + (-5-2i) = -10
so x = -10+5-2i or -10+5+2i\[x = -5\pm2i\]

Answer 3

When y = -5+2i, x = -5-2i
When y = -5-2i, x = -5+2i