Question

Find the values of $x$ and $y$ that satisfy the below given pair of equations, 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 '$a$' and $\frac{1}{y}$ be 'b' (As $x$ $\ne$ 0 & $y$ $\ne$ 0).

We will get our equations as

$2a+3b=13$

$5a-4b=-2$

Multiplying the first equation by 4 and the second equation by 3, we get

$8a+12b=52$

$15a-12b=-6$

Now, adding the two equations, we get

$23a=46$

$a=2$

Substituting $a$ = 2 in the first equation, 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 $y=\frac{1}{3}$.