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Question
Solve the following simultaneous equation.
`2/x + 3/y = 13` ; `5/x - 4/y = -2`
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Solution
`2/x + 3/y = 13` ; `5/x - 4/y = -2`
Let `1/x = u and 1/y = v`
So, the equations obtained are
2u + 3v = 13 ...(I) (× 5)
5u - 4v = -2 ...(II) (× 2)
10u + 15v = 65 ...(III)
10u - 8v = - 4 ...(IV)
Subtracting (IV) from (III)
10u + 15v = 65
10u - 8v = - 4
- + +
23v = 69
⇒ v = 3
Putting the value of v in (I)
∴ 2u + 3v = 13
⇒ 2u + 3 × 3 = 13
⇒ 2u = 4
⇒ u = 2
`1/x = u ⇒ x = 1/u = 1/2`
`1/y = v ⇒ y = 1/v = 1/3`
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