Question

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

Answer 1

Let, p= $\frac{1}{2+x}$ and q = $\frac{1}{y-4}$
Thus, 5p + q = 2---- (i)
6p - 3q = 1-----(ii)

Multiply (i) with 3 and then add the obtained equation to equation (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