Question

Solve the following pairs of equations:

`(5)/(x + y) - (2)/(x - y)` = -1

`(15)/(x + y) + (7)/(x - y)` = 10.

Answer 1

The given equations are `(5)/(x + y) - (2)/(x - y)` = -1 and `(15)/(x + y) + (7)/(x - y)` = 10.

Let `(1)/(x + y) = "a" and (1)/(x - y) = "b"`
Then, we have
5a + 7b = -1       ...(i)
15a + 7b = 10   ....(ii)
Multiplying eqn. (i) by 3, we get
15a - 6b = -3
Subtracting eqn. (iii) from eqn. (ii), we get
13b = 13
⇒ b = 1
Substituting the value of b in eqn. (i), we get
5a - 2(1) = -1
⇒ 5a = 1
⇒ a = `(1)/(5)`
⇒ x + y = 5 and x - y = 1
Adding these two equations, we get
2x = 6
⇒ x = 3
⇒ 3 + y = 5 
⇒ y = 2
Thus, the solution set is (3, 2).