Question

Solve the following pairs of equations:

`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`

`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2

Answer 1

The given equations are `(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)` and `(5)/(3x + 2y) + (1)/(3x - 2y)` = 2.

Let `(1)/(3x + 2y) = "a" and (1)/(3x - 2y) = "b"`
Then, we have
2a + 3b = `(17)/(5)`     ....(i)
5a + b = 2         ....(ii)
Multiplying eqn. (i) by 5 and eqn. (ii) by 2, we get
10a + 15b = 17    ....(iii)
10a + 2b = 4       ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
13b = 13
⇒ b = 1
Substituting the value of b in eqn. (ii), we get
5a + 1 = 2
⇒ 5a = 1
⇒ a = `(1)/(5)`
⇒ 3x + 2y = 5 and 3x - 2y = 1
Adding these two eqations, weget
6x = 6
⇒ x = 1
⇒ 3(1) + 2y = 5
⇒ 2y = 2
⇒ y = 1
Thus, the solution set is (1, 1).