Question

Solve for x and y.. 2/x+y + 5/x-y =3 and 7/x+y -2/x-y =4

Answer 1

Answer:

(9/4,-3/4)

Step-by-step explanation:

Let (1/x+y) be A , and (1/x-y) be B .

now 2A+5B=3 AND  7A -2B=4

By solving we get A = 2/3  ,B= 1/3

i.e. 1/X+Y=2/3 AND 1/X-Y=1/3

THEREFORE X= 9/4 AND Y= -3/4

GOOD LUCK MY BOY(ALL THE BEST MY GIRL).

Answer 2

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

Explanation:

The given system  of equations :

$\dfrac{2}{x+y}+\dfrac{5}{x-y}=3\\\\ \dfrac{7}{x+y}-\dfrac{2}{x-y}=4$

Put $\dfrac{1}{x+y}=u$ and $\dfrac{1}{x-y}=v$ , we get

$2u+5v=3------(1)\\\\7u-2v=4-----------(2)$

Multiply equation (1) by 2 and equation (2) by 5  on both sides, we get

$4u+10v=6 ----(3)$  

$35u-10v=20----(4)$

Add (3) and (4) , we get

$39u=26\\\Rightarrow\ u=\dfrac{26}{39}=\dfrac{2}{3}$

Put this in (1) , we get

$2(\dfrac{2}{3})+5v=3\\\Rightarrow\ v=\dfrac{3-\dfrac{4}{3}}{5}=\dfrac{1}{3}$

So , we get

$\dfrac{1}{x+y}=\dfrac{2}{3}\\\\\Rightarrow\ x+y=\dfrac{3}{2}-------(5)$

$\dfrac{1}{x-y}=\dfrac{1}{3}\\\\\Rightarrow\ x-y=3--------------(6)$

Add (5) and (6) , we get

$2x=\dfrac{9}{2}\Rightarrow\ x=\dfrac{9}{4}$

Subtract (6) from (5) , we get

$2y=-\dfrac{3}{2}\Rightarrow\ y=\dfrac{-3}{4}$

Hence, the value of x is $\dfrac{9}{4}$ and y is $\dfrac{-3}{4}$.

# Learn more :

Solve for x and y:

22/x+y+54/x-y=5

55/x+y+45/x-y=14

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