Question

If $\frac{2}{x}+\frac{3}{y}=2and\frac{6}{x}+\frac{18}{y}=9$, then the values of $x$ and $y$ respectively, are

• A. $3$ and $2$
• B. $2$ and $3$
• C. $4$ and $3$
• D. $3$ and $4$

Answer 1

The correct option is B $2$ and $3$

Let us put $\frac{1}{x}=a$ & $\frac{1}{y}=b$

Then the equations reduce to

$2a+3b=2$ ........(i) &

$6a+18b=9\Rightarrow 2a+6b=3$ .........(ii)

Subtracting (i) from (ii), we get $3b=1$

$⟹b=\frac{1}{3}⟹y=3$

Putting this value of $b$ in (i),

$2a+3\times \frac{1}{3}=2⟹a=\frac{1}{2}⟹x=2.\therefore (x,y)=(2,3)$