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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.

 Jun 3, 2021
 #1
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Real numbers x and y satisfy
x + xy = 250y
x - xy = -240y

 

My attempt:

 

\(\begin{array}{|lrcll|} \hline (1): & x + xy &=& 250y \\ (2): & x - xy &=& -240y \\ \hline (1)+(2):& 2x &=& 10y \quad | \quad :2 \\ &x &=& 5y \quad \text{or} \quad y=\dfrac{x}{5} \\\\ & \dfrac{x}{y} &=& 5 \\ \hline (1):& x + xy &=& 250y \quad|\quad :y \\ & \dfrac{x}{y} + x &=& 250 \\\\ & 5+x &=& 250 \\ & \mathbf{x} &=& \mathbf{245} \\ \hline &y &=& \dfrac{x}{5} \\\\ &y &=& \dfrac{245}{5} \\ & \mathbf{y} &=& \mathbf{49} \\ \hline \end{array}\)

 

laugh

 Jun 3, 2021

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