Question

If $x-y=2\mathrm{and}\frac{2}{x+y}=\frac{1}{5}$ then
(a) x = 4, y = 2 (b) x = 5, y = 3 (c) x = 6, y = 4 (d) x = 7, y = 5

Answer 1

The given system of equations is
$$\begin{gathered} x-y=2.....\left(i\right) \\ x+y=10.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$2x=12\Rightarrow x=6$
Now, putting x = 6 in (ii), we have
$6+y=10\Rightarrow y=10-6=4$
Thus, x = 6 and y = 4.
Hence, the correct answer is option (c).