Question

Solve the following pair of linear equation:
$\frac{5}{2x}+\frac{2}{3y}=7,\frac{3}{x}+\frac{2}{y}=12,x\ne 0,y\ne 0$

• A. $x=\frac{1}{2},y=\frac{1}{4}$
• B. $x=\frac{1}{4},y=\frac{1}{3}$
• C. $x=\frac{1}{2},y=\frac{1}{3}$
• D. $x=\frac{1}{4},y=\frac{1}{6}$

Answer 1

Answer: (C)

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

$\frac{5}{2x}+\frac{2}{3y}=7$ ............... (1)

$\frac{3}{x}+\frac{2}{y}=12$ .................. (2)

Let $\frac{1}{x}=p$ and $\frac{1}{y}=q$

Then, equation (1) and (2) becomes

$\frac{5}{2}p+\frac{2}{3}q=7$ ...................... (3)

$3p+2q=12$ ......................... (4)

Further simplifying (3),

$15p+4q=42$ ............. (5)

Multiplying equation (4) with $2$ ,

$6p+4q=24$ ................. (6)

Subtract (6) from (5),

$15p-6p=42-24$

$9p=18$

$p=2$

$\Rightarrow x=\frac{1}{2}$

From equation (4),

$2q=12-3p$

$2q=12-6$

$2q=6$

$q=3$

$\Rightarrow y=\frac{1}{3}$