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## anonymous 5 years ago 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.

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1. anonymous

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.

2. anonymous

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$x = -5\pm2i$

3. anonymous

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

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