Question

Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{4}{x}+3y=14$ , $\frac{3}{x}-4y=23$

Answer 1

The given pair of equations are $\frac{4}{x}+3y=14$ and $\frac{3}{x}-4y=23$

Put $\frac{1}{x}=u$ we get $4u+3y=14...\left(1\right),3u-4y=23...\left(2\right)$

From $\left(1\right)$ we get $u=\frac{14-3y}{4}$

Substitute $u$ in $\left(2\right)$ we get

$3\left(\frac{14-3y}{4}\right)-4y=23$

$\Rightarrow 42-9y-16y=92$

$\Rightarrow -25y=50$

$\Rightarrow y=-2$

Substitute $y=-2$ in $u=\frac{14-3y}{4}$ we get $u=5$

Hence $\frac{1}{x}=u=5\Rightarrow x=\frac{1}{5}$

Solution: $x=\frac{1}{5},y=-2$