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# System

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Real numbers x and y satisfy

x + xy = 250y

x - xy = 240y

Enter all possible values of x, separated by commas.

Oct 21, 2021

### 1+0 Answers

#1
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x + xy = 250y

x - xy = 240y

Enter all possible values of x, separated by commas.

Hello Guest!

$$x + xy = 250y\\ x(1+y)=250y\\ x - xy = 240y\\ x(1-y)=240y$$

$$\frac{250y}{1+y}=\frac{240y}{1-y}\\ 250y-250y^2=240y+240y^2\\ 10y=490y^2\\ 0=y(490y-10)$$

$$\large y\in \{0,\dfrac{1}{49}\}$$

$$x=\dfrac{250y}{1+y}$$

$$x=\dfrac{250\cdot \dfrac{1}{49} }{1+\dfrac{1}{49}}=\dfrac{250}{49}\cdot \dfrac{49}{50}=5$$

$$\large x\in \{0,5\}$$

!

Oct 21, 2021