Question

Based on equations reducible to linear equations
Solve for x and y $\frac{1}{3x}-\frac{1}{7y}=\frac{2}{3};\frac{1}{2x}-\frac{1}{3y}=\frac{1}{6}$

• A. $x=1/8,y=1/2$
• B. $x=1/3,y=1/6$
• C. $x=1/7,y=1/8$
• D. $x=1/5,y=1/7$

Answer 1

The correct option is D $x=1/5,y=1/7$

The given equations are
$\Rightarrow \frac{1}{3x}-\frac{1}{7y}=\frac{2}{3}....eq\left(1\right)$
$\Rightarrow \frac{1}{2x}-\frac{1}{3y}=\frac{1}{6}....eq\left(2\right)$
Put $\frac{1}{x}=u$ and $\frac{1}{y}=v$ in $eq\left(1\right)$ and $eq\left(2\right)$
$\Rightarrow \frac{1}{3}u-\frac{1}{7}v=\frac{2}{3}\Rightarrow 7u-3v=\mathrm{14....}eq\left(3\right)$
$\Rightarrow \frac{1}{2}u-\frac{1}{3}v=\frac{1}{6}\Rightarrow 3u-2v=\mathrm{1....}eq\left(4\right)$
$Substracteq\left(3\right)andeq\left(4\right)$
$\Rightarrow 5u=25\Rightarrow u=5$
$putthevalueofuineq\left(3\right)$
$\Rightarrow 7\times 5-3v=14\Rightarrow v=7$
$Hence,\frac{1}{x}=u=5\Rightarrow x=\frac{1}{5}$
$\frac{1}{y}=v=7\Rightarrow y=\frac{1}{7}$