If 2 x +3 y =6 and 1 x +1 2y =2 then : - Vidyadip

MCQ

If $\frac{2}{\text{x}}+\frac{3}{\text{y}}=6$ and $\frac{1}{\text{x}}+\frac{1}{2\text{y}}=2$ then :

A
$\text{x}=1,\ \text{y}=\frac{2}{3}$
✓
$\text{x}=\frac{2}{3},\ \text{y}=1$
C
$\text{x}=1,\ \text{y}=\frac{3}{2}$
D
$\text{x}=\frac{3}{2},\ \text{y}=1$

✓

Answer

Correct option: B.

$\text{x}=\frac{2}{3},\ \text{y}=1$

$\frac{2}{\text{x}}+\frac{3}{\text{y}}=6$ and $\frac{1}{\text{x}}+\frac{1}{2\text{y}}=2$
Multiplying $\frac{1}{\text{x}}+\frac{1}{2\text{y}}=2$ by $2,$ we get $\frac{2}{\text{x}}+\frac{1}{\text{y}}=4$
So, we have equations, $\frac{2}{\text{x}}+\frac{3}{\text{y}}=6$ and $\frac{2}{\text{x}}+\frac{1}{\text{y}}=4$
Put $\frac{1}{\text{x}}=\text{u}$ and $\frac{1}{\text{y}}=\text{v}$
So, we get
$2u + 3v = 6 ...(i)$
$2u + v = 4 ....(ii)$
Substituting $v = 1$ in $(ii),$ we get $\text{u}=\frac{3}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{3}{2}$ and $\frac{1}{\text{y}}=1$
$\Rightarrow\text{x}=\frac{2}{3}$ and $\text{y}=1.$

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