Question

2/x+y+5/x-y=3;7/x+y-2/x-y=4

Answer 1

Answer:

2/x+y+5/x-y=3 ;7/x+y-2/x-

2/x+5/x=3

2+5/x=3

7/x=3

3x=7

x=7/3

Answer 2

The value of $x=\dfrac{9}{4}$ and $y=-\dfrac{3}{4}$

Step-by-step explanation:

Given:

$\dfrac{2}{x+y}+\dfrac{5}{x-y}=3$

$\dfrac{7}{x+y}-\dfrac{2}{x-y}=4$

This is two variable system of linear equation.

Let $\dfrac{1}{x+y}=u$  and  $\dfrac{1}{x-y}=v$

$2u+5v=3$

$7u-2v=4$

Using elimination method, eliminate v

$2u+5v=3]\times 2$

$7u-2v=4\times 5$

$4u+10v=6$

$35u-10v=20$

Add both equation

$39u=26$

$u=\dfrac{2}{3}$

$v=\dfrac{1}{3}$

So, $x+y=\dfrac{3}{2}$    and $x-y=3$

Add both equation and eliminate y

$2x=\dfrac{3}{2}+3$

$x=\dfrac{9}{4}$

$\dfrac{9}{4}+y=\dfrac{3}{2}$

$y=-\dfrac{3}{4}$

#Learn more:

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