Question

Solve 5/x+1-2/y-1=1/2,10/x+1+2/y-1=5/2

Answer 1

Answer:

Let 1/x be u and 1/y be v

therefore,

5u-2v=1/2...........eqn(i)

10u+2v=5/2.......eqn(ii)

on solving (i) and (ii)

-2v and +2v gets canceled

hence,

15u=3

u=3/15

u=1/5

u=1/5

1/x=1/5

therefore x=5

substituting x=5 in 5/x+1-2/y-1=1/2

5/5-2y=1/2

1-2y=1/2

taking LCM

y-2/y=1/2

cross multiplying

2y-2=y

2y-y=2

y=2

hence x=5 and y=2

hope it helps......

please mark as the brainliest

Answer 2

Answer:

x = 4, y = 5

Step-by-step explanation:

Given, $\frac{5}{x+1}$ - $\frac{2}{y-1}$  = $\frac{1}{2}$  and  $\frac{10}{x+1}$ + $\frac{2}{y-1}$ = $\frac{5}{2}$

To Find: Solution of the given equation.

Solution:

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

So, the equations become,

5u - 2v = $\frac{1}{2}$  ----(1)  and 10u + 2v = $\frac{5}{2}$  -----(2)

Adding both equations,

⇒ 5u -2v + 10u + 2v = $\frac{1}{2}$ + $\frac{5}{2}$

⇒ 15u = $\frac{6}{2}$

⇒ 15u = 3

⇒ u = $\frac{1}{5}$

Putting u in equation (1),

⇒ 5 × $\frac{1}{5}$ - 2v = $\frac{1}{2}$

⇒ 2v = 1 - $\frac{1}{2}$

⇒ v = $\frac{1}{2}$ × $\frac{1}{2}$

⇒ v =$\frac{1}{4}$

Now,

⇒ u = $\frac{1}{x+1}$   and  ⇒ v =$\frac{1}{y-1}$

⇒ x + 1 = $\frac{1}{\frac{1}{5} }$  and  ⇒ y - 1 = $\frac{1}{\frac{1}{4} }$

⇒ x = 5 - 1 and  ⇒ y = 4 + 1

⇒ x = 4 and ⇒ y = 5

Hence, solution of the given equations is x= 4, y =5.

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