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Question
Solve the following pairs of equations:
`(3)/x - (1)/y` = -9
`(2)/x + (3)/y` = 5
Solution
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)`.
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