Question

Solve the following pair of equation by reducing them to a pair of linear equations
$\frac{3}{x}+\frac{7}{y}=14$ and $\frac{2}{x}+\frac{7}{y}=21$

• A. $5$ and $\frac{-7}{2}$
• B. $\frac{1}{7}$ and $5$
• C. $5$ and $-7$
• D. $\frac{-1}{7}$ and $\frac{1}{5}$

Answer 1

The correct option is D $\frac{-1}{7}$ and $\frac{1}{5}$

The given equation can be written as
$3\left(\frac{1}{x}\right)+7\left(\frac{1}{y}\right)=14$
$2\left(\frac{1}{x}\right)+7\left(\frac{1}{y}\right)=21$
Let assume $\frac{1}{x}=a;\frac{1}{y}=b$
$3a+7b=14$ ----- (1)
$2a+7b=21$ ----- (2)
Subtracting the equation (1) and (2) we get
$3a+7b=14$
$2a+7b=21$
(-) (-) (-)
____________
$a=-7$
Put the value of a in equation (2)
$2(-7)+7b=21$
$-14+7b=21$
$7b=21+14$
$7b=35$
$b=\frac{35}{7}=5$
$\therefore \frac{1}{x}=a;\frac{1}{y}=b$
$\frac{1}{x}=-7;\frac{1}{y}=5$
Hence $x=\frac{1}{-7};y=\frac{1}{5}$