Question

Solve the following pairs of equations:

`(3)/x - (1)/y` = -9

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

Answer 1

The given equations are `(3)/x - (1)/y` = -9 and `(2)/x + (3)/y` = 5

Let `(1)/x = "a" and (1)/y = "b"`
Then, we have 
3a - b = -9    ....(i)
2a + 3b = 5  ....(ii)
Multiplying eqn. (i) by 3, we get
9a - 3b = -27  ....(iii)
Adding eqns. (ii) and (iii), we get
11a = -22
⇒ a = -2
⇒`(1)/x` = -2
⇒ x = `-(1)/(2)`
Substituting the value of a in eqn. (i), we get
3(-2) -b = -9
⇒ -6 - b = -9
⇒ b = -6 + 9
⇒ b = 3
⇒ `(1)/y` = 3
⇒ y = `(1)/(3)`
Thus, the solution set is `(-1/2, 1/3)`.