Question

find the values of x and y from the following equations 7/x+y +6/x-y =7 ;4/x-y - 14/x+y =2​

Answer 1

Solution :-

→ (7/x+y) + (6/x-y) = 7

→ (4/x-y) - (14/x+y) = 2

Let,

• 1/(x + y) = m .
• 1/(x - y) = n .

putting both we get,

→ 7m + 6n = 7 ----------- Eqn.(1)

→ 4n - 14m = 2 ---------- Eqn.(2)

Multiply Eqn.(1) by 2 and adding in Eqn.(2) we get,

→ 2(7m + 6n) + (4n - 14m) = 2*7 + 2

→ 14m - 14m + 12n + 4n = 14 + 2

→ 16n = 16

dividing both sides by 16,

→ n = 1.

Putting value of n in Eqn.(1),

→ 7m + 6*1 = 7

→ 7m = 7 - 6

→ 7m = 1

dividing both sides by 7,

→ m = (1/7) .

Therefore,

→ 1/(x + y) = m

→ 1/(x + y) = (1/7)

→ (x + y) = 7 ----------- Eqn.(3)

and,

→ 1/(x - y) = n

→ 1/(x - y) = 1

→ (x - y) = 1 ----------- Eqn.(4)

Adding Eqn.(3) and Eqn.(4) , we get,

→ (x + y) + (x - y) = 7 + 1

→ x + x + y - y = 8

→ 2x = 8

dividing both sides by 2,

→ x = 4. (Ans.)

Putting value of x in Eqn.(3) ,

→ 4 + y = 7

→ y = 7 - 4

→ y = 3. (Ans.)

Hence, value of x is 4 and value of y is 3.

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