Question

Question 1 (iii)
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

$\frac{4}{x}+3y=14$
$\frac{3}{x}-4y=23$
Putting $\frac{1}{x}=p$ in the given equations, we get
4p + 3y = 14
$\Rightarrow$ 4p + 3y - 14 = 0 ---(i)
$\Rightarrow$ 3p - 4y -23 = 0 ---(ii)
By cross-multiplication, we get
$\frac{p}{-69-56}=\frac{y}{-42-(-92)}=\frac{1}{-16-9}$
$\Rightarrow \frac{-p}{125}=\frac{y}{50}=\frac{-1}{25}$
Now, $\frac{-p}{125}=\frac{-1}{25}$ and
$\frac{y}{50}=\frac{-1}{25}$
$\Rightarrow$ p = 5 and y = -2
Also, $p=\frac{1}{x}=5$
$\Rightarrow x=\frac{1}{5}$
So, $x=\frac{1}{5}$ and y = -2 is the solution.