An algebra problem by Aly Ahmed

Algebra Level 2

Find the solution of ( x , y ) (x,y) satisfying the system of equations below:

{ 4 x − 5 y = x + y x y + 57 35 x y = 35 34 ( y − x ) \large \begin{cases} \tfrac4x - \tfrac5y = \tfrac{x+y}{xy} + \tfrac{57}{35} \\ xy = \tfrac{35}{34} (y-x) \end{cases}

( 2 , 2 ) (2,2) ( 0 , 0 ) (0,0) ( 1 , 1 ) (1,1) ( 5 7 , 7 3 ) \left(\frac57, \frac73\right)

Aly Ahmed by Aly Ahmed , 34, Egypt

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1 solution

In reduced form, the equations are :

1 x − 2 y = 19 35 \dfrac 1x -\dfrac 2y =\dfrac {19}{35}

1 x − 1 y = 34 35 \dfrac 1x -\dfrac 1y =\dfrac {34}{35}

Solving we get

x = 5 7 , y = 7 3 x=\dfrac 57,y=\dfrac 73

Hence ( x , y ) = ( 5 7 , 7 3 ) (x, y) =\boxed {\left (\dfrac 57,\dfrac 73\right )} .

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I wish the question had latex.

Kano Boom - 10 months, 3 weeks ago

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I think he is weak in latex, or is lazy enough to use that.

A Former Brilliant Member - 10 months, 3 weeks ago

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