Question

Solve the following pair of equation by reducing them to a pair of linear equations
$\frac{3}{x}+4y=43$ and $\frac{-2}{x}+3y=11$

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

Answer 1

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

The given equation can be written as
$3\left(\frac{1}{x}\right)+4\left(y\right)=43$

$-2\left(\frac{1}{x}\right)+3\left(y\right)=11$

Let assume $\frac{1}{x}=m;\frac{1}{y}=n$

$3m+4n=43$ ----- (1)
$-2m+3n=11$ ----- (2)
Multiply equation (1) by 2 and equation (2) by 3 and then subtract the equation
$6m+8n=86$
$-6m+9n=33$
_______________
$17n=119$

$n=\frac{119}{17}=7$
Put the value of n in equation (1)
$3m+4\left(7\right)=43$
$3m+28=43$
$3m=43-28$
$3m=15$

$m=\frac{15}{3}=5$

$\therefore \frac{1}{x}=m;y=n$

$\frac{1}{x}=5;y=7$
Hence $x=\frac{1}{5};y=7$