Question

Find the values of x and y in the below given pair of equation, where $x\ne 0\&y\ne 0$.
$\frac{2}{x}+\frac{3}{y}=13$
$\frac{5}{x}-\frac{4}{y}=-2$

Answer 1

$Let\frac{1}{x}be{}^{\prime }{a}^{\prime }and\frac{1}{y}be{}^{\prime }{b}^{\prime }(Asx\ne 0andy\ne 0)$.

We will get our equations as

$2a+3b=13------\left(i\right)$

$5a-4b=-2----\left(ii\right)$

Multiplying the $\left(i\right)$ by 4 and the $\left(ii\right)$ by 3, we get

$8a+12b=52----\left(iii\right)$

$15a-12b=-6---\left(iv\right)$

Now adding the two equations, we get

$23a=46$

$a=2$

Substituting a = 2 in the $\left(i\right)$, we get

2 × 2 + 3b = 13

3b = 9

$\Rightarrow$b = 3


Earlier we have assumed that $a=\frac{1}{x}$ & $b=\frac{1}{y}$

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