Question

Solve the following system of equations by elimination method.

$\frac{3}{x}+\frac{5}{y}=\frac{20}{xy},\frac{2}{x}+\frac{5}{y}=\frac{15}{xy},x\ne 0,y\ne 0$

• A. $(1,5)$
• B. $(2,5)$
• C. $(1,2)$
• D. None of these

Answer 1

The correct option is A $(1,5)$

Consider the given equations.

$\frac{3}{x}+\frac{5}{y}=\frac{20}{xy}$

$5x+3y=20$ $-------\left(1\right)$

$\frac{2}{x}+\frac{5}{y}=\frac{15}{xy}$

$5x+2y=15$ $-------\left(2\right)$

Subtract $\left(1\right)$ and $\left(2\right)$

$5x+3y=20$

$5x+2y=15$

—————————

$y=5$ $[$ put in $\left(2\right)]$

$5x+2\times 5=15$

$5x+10=15$

$5x=5$

$x=1$

Hence, the value of $x$ is $1$ and the value of $y$ is $5$.