Question

Based on equations reducible to linear equations
Solve for x and y: $\frac{11}{2x}-\frac{9}{2y}=-\frac{23}{2};\frac{3}{4x}+\frac{7}{15y}=\frac{23}{6}$

• A. $x=1/2,y=1/5$
• B. $x=1/5,y=1/9$
• C. $x=1/7,y=1/2$
• D. $x=1/3,y=1/4$

Answer 1

The correct option is A $x=1/2,y=1/5$

The given equations are
$\Rightarrow \frac{11}{2x}-\frac{9}{2y}=-\frac{23}{2}....eq\left(1\right)$

$\Rightarrow \frac{3}{4x}+\frac{7}{15y}=-\frac{23}{6}....eq\left(2\right)$

Put $u=\frac{1}{x}$ and $v=\frac{1}{y}$ in $eq\left(1\right)$ and $\left(2\right)$

$\Rightarrow \frac{11}{2}u-\frac{9}{2}v=-\frac{23}{2}\Rightarrow 11u-9v=-\mathrm{23....}eq\left(3\right)$

$\Rightarrow \frac{3}{4}u+\frac{7}{15}v=\frac{23}{6}\Rightarrow 45u+28v=230....eq\left(4\right)$

Multiply $eq\left(3\right)$ by 28 and $eq\left(4\right)$ by 9 and subtract both

$\Rightarrow (308u-252v=-644)-(405u+252v=2070)$

$\Rightarrow 713u=1426\Rightarrow u=2$

$Putu=2ineq\left(3\right)$

$\Rightarrow 11\times 2-9v=-23\Rightarrow v=5$

$Hence,\frac{1}{x}=u=2\Rightarrow x=\frac{1}{2}$
$\frac{1}{y}=v=5\Rightarrow y=\frac{1}{5}$