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# Algebra

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Real numbers x and y satisfy

x + xy = 250y

x - xy = -240y

Enter all possible values of y, separated by commas.

Jan 31, 2022

#1
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For starters, $$y=0$$, because then $$x=0$$.

However, there is more than $$1$$ solution.

Here is the work in LaTex:

$$x+xy=250y$$

$$x=250y-xy$$

$$x=(250-x)y$$

$${x\over{250-x}} = y$$

$$x- {{x^2}\over{250-x}}=-240{x\over{250-x}}$$

$$x- {{x^2}\over{250-x}}={-240x\over{250-x}}$$

$$x={{-240x+x^2}\over250-x}$$

$$250x-x^2=-240x+x^2$$

$$490x=2x^2$$

$$245x=x^2$$

$$x=245$$

Plug it in to the equation:

$$245+245y=250y$$

$$245 = 5y$$

$$y=49$$

This means that the two answers are$$\color{brown}\boxed {y=0,y=49}$$

Jan 31, 2022