Question

Solve the following pairs of equations:

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

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

Answer 1

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

Let `(1)/x = "a" and (1)/y = "b"`
Then, we have
`(3)/(2)"a" + (2)/(3)"b"` = 5
⇒ 9a + 4b = 30    ....(i)
And, 5a - 3b = 1  ....(ii)
Multiplying eqn. (i) by 3 and eqn. (ii) by 4, we get
27a + 12b = 90   ....(iii)
20a - 12b = 4     ....(iv)
Adding rqns. (iii) and (iv), we get
47a = 94
⇒ a = 2
⇒ `(1)/x ` = 2
⇒ x = `(1)/(2)`
Substituting the value of a (i), we get
9(2) + 4b = 30
⇒ 18 + 4b = 30
⇒ 4b = 12
⇒ b = 3
⇒ `(1)/y` = 3
⇒ y = `(1)/(3)`
Thus, the solution set is `(1/2, 1/3)`.