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Question
Solve the following pairs of equations by reducing them to a pair of linear equations
`4/x + 3y = 14`
`3/x - 4y = 23`
Solution
4/x + 3y = 14
3/x - 4y = 23
Putting 1/x = p in the given equations, we get
4p + 3y = 14 ⇒ 4p + 3y - 14 = 0
3p - 4y = 23 ⇒ 3p - 4y -23 = 0
By cross-multiplication, we get
`p/(-69-56) = y/(-42-(-92)) = 1/(-16-9)`
⇒ `(-p)/125 = y/50 = (-1)/25`
Now,
`(-p)/125 = (-1)/25 and y/50 = (-1)/25`
⇒ p = 5 and y = -2
Also, `p = 1/x = 5`
⇒ `x = 1/5`
So, `x = 1/5` and y = -2 is the solution.
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