Question

Solve the following simultaneous equations: $\frac{1}{3x}-\frac{1}{4y}+1=0;\frac{1}{5x}+\frac{1}{2y}=\frac{4}{15}$.

Answer 1

Given:

$\frac{1}{3x}-\frac{1}{4y}+1=0;\frac{1}{5x}+\frac{1}{2y}=\frac{4}{15}$

Assuming,

$\frac{1}{x}=X,\frac{1}{y}=Y$, we get

from the first equation

$\frac{X}{3}-\frac{Y}{4}+1=0$

$\Rightarrow 4X-3Y+12=0$ ...(1)

from the second equation

$\frac{X}{5}+\frac{Y}{2}=\frac{4}{15}$

multiply by 30 on both sides we get

$\Rightarrow 6X+15Y=8$ ...(2)

Now, Multiplying (1) by 5 and then add (2) to it, we get

$26X+52=0$

$\Rightarrow X=-2$

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

$Y=\frac{4}{3}$

$\Rightarrow \frac{1}{y}=\frac{4}{3}\Rightarrow y=\frac{3}{4}$