Question

Solve the following pair of simultaneous equations:

$\frac{1}{x}+\frac{1}{y}=5;\frac{1}{x}-\frac{1}{y}=1$

• A. $x=\frac{3}{2};y=\frac{3}{4}$
• B. $x=\frac{1}{2};y=\frac{2}{3}$
• C. $x=\frac{1}{3};y=\frac{1}{2}$
• D. $x=\frac{2}{3};y=\frac{1}{2}$

Answer 1

The correct option is C $x=\frac{1}{3};y=\frac{1}{2}$

Let $\frac{1}{x}=u$ and $\frac{1}{y}=v$

So, it becomes $u+v=5$ and $u-v=1$

Adding the both equations, $2u=6$ and $u=3$.

Substituting $u$ in either of the equations, we get $v=2$.

So, $\frac{1}{x}=3$ and $\frac{1}{y}=2$

$x=\frac{1}{3}$ and $y=\frac{1}{2}$.

Option $C$