Question

Solve the following simultaneous equations:

$\frac{1}{x}+\frac{1}{y}=8;\frac{4}{x}-\frac{2}{y}=2$

• A. $x=\frac{1}{3},y=\frac{1}{5}$
• B. $x=\frac{1}{2},y=\frac{1}{5}$
• C. $x=\frac{1}{3},y=\frac{1}{7}$
• D. $x=\frac{1}{2},y=\frac{1}{7}$

Answer 1

The correct option is A $x=\frac{1}{3},y=\frac{1}{5}$

Given equations are

$\frac{1}{x}+\frac{1}{y}=8\frac{4}{x}-\frac{2}{y}=2$

Let $\frac{1}{x}=a,\frac{1}{y}=b$

So, $a+b=8$ ....... $\left(1\right)$

$4a-2b=2$ ...... $\left(2\right)$

Multiply equation $\left(1\right)$ by $2$, we get

$2a+2b=16$ ........ $\left(3\right)$

Adding equations $\left(2\right)$ and $\left(3\right)$, we get

$6a=18$

$a=\frac{18}{6}=3$

Put $a=3$ in $a+b=8$

we get $b=5$

So $x=\frac{1}{3}$ and $y=\frac{1}{5}$