MCQ
If $\frac{1}{x}+\frac{2}{y}=4$ and $\frac{3}{y}-\frac{1}{x}=11$ then
- A$x =2, y =3$
- B$x =-2, y =\frac{1}{3}$
- C$x =-\frac{1}{2}, y =3$
- ✓$x =-\frac{1}{2}, y =\frac{1}{3}$
✓
Answer
Correct option: D.
$x =-\frac{1}{2}, y =\frac{1}{3}$
Putting $\frac{1}{ x }= u$ and $\frac{1}{ y }= v$
$\therefore u+2 v=4 \ldots \ldots(i)$
and $3 v-u=11$
$-u+3 v=11 \ldots \ldots(ii)$
On solving eq. $(i)$ and $(ii)$
$u+2 v=4$
$-u+3 v=11$
$5 v=15$
$\Rightarrow v=\frac{15}{5}=3$
Putting the value of $v$ in eq. $(i)$
$u+2 \times 3=4$
$\Rightarrow u =4-6=-2$
$\because \frac{1}{ x }= u$
$\Rightarrow x =\frac{1}{ u }=\frac{1}{-2}=-\frac{1}{2}$ and
$\frac{1}{ y }= v$
$\Rightarrow y =\frac{1}{ v }=\frac{1}{3}$
$\therefore x =-\frac{1}{2}$ and $y =\frac{1}{3}$
$\therefore u+2 v=4 \ldots \ldots(i)$
and $3 v-u=11$
$-u+3 v=11 \ldots \ldots(ii)$
On solving eq. $(i)$ and $(ii)$
$u+2 v=4$
$-u+3 v=11$
$5 v=15$
$\Rightarrow v=\frac{15}{5}=3$
Putting the value of $v$ in eq. $(i)$
$u+2 \times 3=4$
$\Rightarrow u =4-6=-2$
$\because \frac{1}{ x }= u$
$\Rightarrow x =\frac{1}{ u }=\frac{1}{-2}=-\frac{1}{2}$ and
$\frac{1}{ y }= v$
$\Rightarrow y =\frac{1}{ v }=\frac{1}{3}$
$\therefore x =-\frac{1}{2}$ and $y =\frac{1}{3}$
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