Question

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{7x-2y}{xy}=5$

$\frac{8x+7y}{xy}=15$

Answer 1

The pair of equations is given as,

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

$7x-2y=5xy$ (1)

And,

$\frac{8x+7y}{xy}=15$

$8x+7y=15xy$ (2)

From equation (1) and (2),

$-65y=-65xy$

$x=1$

Substituting the value of $x$ in equation (1),

$7\left(1\right)-2y=5\left(1\right)y$

$7-2y=5y$

$7=7y$

$y=1$

Therefore, the values are $x=1$ and $y=1$.