MCQ
If $\frac{1}{\text{x}}+\frac{2}{\text{y}}=4$ and $\frac{3}{\text{y}}+\frac{1}{\text{x}}=11$ then :
- ✓$\text{x}=2,\ \text{y}=3$
- B$\text{x}=-2,\ \text{y}=3$
- C$\text{x}=\frac{-1}{2},\ \text{y}=3$
- D$\text{x}=\frac{-1}{2},\ \text{y}=\frac{1}{3}$
✓
Answer
Correct option: A.
$\text{x}=2,\ \text{y}=3$
$\frac{2\text{x}}{3}-\frac{\text{y}}{2}+\frac{1}{6}=0$
Multiply by the $\text{LCM}, 6.$
$\Rightarrow 4x - 3y + 1 = 0$
$\Rightarrow 4x - 3y = -1 ....(i)$
$\frac{\text{x}}{2}+\frac{2\text{y}}{3}=3$
Multiply by the $\text{LCM}, 6.$
$3x + 4y = 18 ...(ii)$
Multiply equation $(i)$ and $(ii) $ by $4$ and $3$ respectively.
$16x - 12y = -4 ...(iii)$
$9x + 12y = 54 ...(iv)$
Adding equations $(iii)$ and $(iv),$ we get
$25x = 50$
$\Rightarrow x = 2$
Substituting $x = 2$ in $(ii),$ we get $y = 3$.
Multiply by the $\text{LCM}, 6.$
$\Rightarrow 4x - 3y + 1 = 0$
$\Rightarrow 4x - 3y = -1 ....(i)$
$\frac{\text{x}}{2}+\frac{2\text{y}}{3}=3$
Multiply by the $\text{LCM}, 6.$
$3x + 4y = 18 ...(ii)$
Multiply equation $(i)$ and $(ii) $ by $4$ and $3$ respectively.
$16x - 12y = -4 ...(iii)$
$9x + 12y = 54 ...(iv)$
Adding equations $(iii)$ and $(iv),$ we get
$25x = 50$
$\Rightarrow x = 2$
Substituting $x = 2$ in $(ii),$ we get $y = 3$.
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