Question

Does anyone know the answer for this ?

Answer 1

Question

Solve :-

2/(x+y) + 3/(x-y) = 1 , 8/(x+y) - 7/(x-y) = 5/6

Solution

Given:-

• 2/(x+y) + 3/(x-y) = 1---------------(1)
• 8/(x+y) - 7/(x-y) = 5/6 ---------(2)

Find:-

• Value of x and y

Explanation:-

Let,

• 1/(x+y) = m
• 1/(x-y) = n

So,

• 2m + 3n = 1 ---------------(3)
• 8m - 7n = 5/6-------------(4)

Multiply by 8 in equ(3) and 2 in equ(4)

• 16m + 24n = 8
• 16m - 14n = 5/3

______________ Sub, it's

➤▸ 24n + 14n = 8 - 5/3

➤▸ 38n = (24-5)/3

➤▸ 38n = 19/3

➤▸ n = 19/(38 * 3)

➤▸ n = 1/6

Keep value of n in equ(3),

➤▸ 2m + 3 * 1/6 = 1

➤▸ 2m = 1 - 1/2

➤▸ 2m = (2-1)/2

➤▸ m = 1/4

Hence,

• 1/(x+y) = m = 1/4
• 1/(x-y) = n = 1/6

We can write this,

• x + y = 4 ----------(5)
• x - y = 6 ------------(6)

____________add it's

➤▸ 2x = 10

➤▸ x = 10/2

➤▸ x = 5

keep value in equ(5)

➤▸ 5 + y = 4

➤▸y = 4 - 5

➤▸ y = -1

Hence:-

• Value of x = 5 [ Ans.]
• Value of y = -1. [ Ans]

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