Question

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

• A. $x=12/5,y=6/5$
• B. $x=2/5,y=1/5$
• C. $x=9,y=9/2$
• D. $x=2,y=1$

Answer 1

The correct option is A $x=12/5,y=6/5$

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

$\Rightarrow 7x-2y=5xy$

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

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

Substitute $x=2y$ in the above equation, we get

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

$\Rightarrow \frac{14-2}{2y}=5$

$\Rightarrow \frac{12}{2y}=5y$

$\Rightarrow 5y=6$

$\therefore y=\frac{6}{5}$

Put $y=\frac{6}{5}$ in $x=2y$ we get

$x=2\times \frac{6}{5}=\frac{12}{5}$

$\therefore x=\frac{12}{5},y=\frac{6}{5}$