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, 5p + q = 2---- (i)
6p - 3q = 1-----(ii)

Multiply Eq (i) by 3 $\Rightarrow$ 15p + 3q = 6.......(iii)

Adding (ii) and (iii), and solving the two equations we get p= $\frac{1}{3}$ and q = $\frac{1}{3}$

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