Question

Find the value of x and y for the pair of equations $\frac{7x-2y}{xy}=5$ and $\frac{8x-6y}{xy}=15$

• A. 2, not defined
• B. , not defined
• C. - , not defined
• D. None of these

Answer 1

The correct option is C

- , not defined

First separate the variables

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

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

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

Similarly, separate of variables of the second equation

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

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

Now we see that the equation is not linear.

Therefore, substitute $\frac{1}{x}$ = u and $\frac{1}{y}$ = v

The pair of equation can be written as

-2u+7v=5

-6u+8v=15

Using the method of elimination

-6u+21v=15

-6u+8v = 15

We get u= - $\frac{5}{2}$ v=0

As we have assumed $\frac{1}{x}$ = u and $\frac{1}{y}$ = v

x= - $\frac{2}{5}$ and y= not defined.