Question

7/2x+1+13/y+2=27 and 13/2x+1+7/y+2=33

Answer 1

Ans.

$\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 \: \: ...(1) \\ \frac{13}{2x + 1} + \frac{7}{y + 2} = 33 \: \: ...(2)$
We multiply (1) by 13 and (2) by 7.
Then
$\frac{91}{2x + 1} + \frac{169}{y + 2} = 351 \\ \frac{91}{2x + 1} + \frac{49}{y + 2} = 231$
Subtracting, we get
$\frac{120}{y + 2} = 120 \\ or \: \: y + 2 = 1 \\ or \: \: y = - 1$
From (1), we get
$x = - \frac{1}{4}$
Hence, the required solution is
$x = - \frac{1}{4} \: \: \: and \: \: \: y = - 1$

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