Question

Solve the following pair of equations.

$\frac{7x-2y}{xy}=5$

$\frac{8x+6y}{xy}=15$

Here, x $\ne$ 0 and y $\ne$ 0.

• A. x = 2, y = -5
• B. $x=\frac{5}{2},\text{y is not defined}$
• C. $x=-\frac{2}{5},\text{y is not defined}$
• D. $x=\frac{4}{3},y=\frac{7}{2}$

Answer 1

The correct option is C

$x=-\frac{2}{5},\text{y is not defined}$

$\frac{7x-2y}{xy}=5$

$\Rightarrow \frac{7x}{xy}-\frac{2y}{xy}=5$

$\Rightarrow \frac{7}{y}-\frac{2}{x}=5$

Similarly we can do the same for the second equation.

$\frac{8x+6y}{xy}=15$

$\Rightarrow \frac{8}{y}-\frac{6}{x}=15$

Now we can see that the equation is not linear. So we will assume $\frac{1}{x}=u$ and $\frac{1}{y}=v$

So, the pair of equation can be written as

-2u + 7v = 5

-6u + 8v = 15

We can solve the pair of equation by method of elimination.

On multiplying equation -2u + 7v = 5 by 3 we get

-6u + 21v = 15 ...(1)

-6u + 8v = 15 ...(2) (given)

On subtracting equation (2) from equation (1), we get 13v = 0 i.e. v = 0

On substituing v = 0 in equation -2u + 7v = 5, we get

$u=-\frac{5}{2}$

We know that $\frac{1}{x}=u\text{and}\frac{1}{y}=v$

$\therefore x=-\frac{2}{5}$

and $y=\frac{1}{0}$, which is not defined.