Question

Solving $\frac{5}{2+x}+\frac{1}{y-4}=2$; $\frac{6}{2+x}-\frac{3}{y-4}=1,$
we get

x = ___
y = ___

Answer 1

Let, p= $\frac{1}{2+x}$ and q = $\frac{1}{y-4}$

Thus, given equations reduce to,

$5p+q=2$---- (i)

$6p-3q=1$-----(ii)

Multiply (i) with 3 then add with (ii), we get

$p=\frac{1}{3}$ and $q=\frac{1}{3}$

Now, $p=\frac{1}{2+x}$

$\Rightarrow \frac{1}{3}=\frac{1}{2+x}$

$\Rightarrow x=1$

$q=\frac{1}{y-4}$

$\Rightarrow \frac{1}{3}=\frac{1}{y-4}$

$\Rightarrow y=7$