Question

Solve:

3/x + 12/y =5/2 ; 6/X +8/y=1​

Answer 1

Solution:-

We have

$\rm \implies \: \dfrac{3}{x} + \dfrac{12}{y} = \dfrac{5}{2} \: \: \: \: \: \: ...(i)eq$

$\rm \implies \: \dfrac{6}{x} + \dfrac{8}{y} = 1 \: \: \: \: \: \: ...(ii)eq$

Now let

$\rm \implies \: \dfrac{1}{x} = u \: \: and \: \: \dfrac{1}{y} = v$

We get

$\rm \implies \: 3u + 12v = \dfrac{5}{2} \: \: ....(i)eq$

$\rm \implies \: 6u + 24v = 5 \: \: \: ....(i)eq$

$\rm \implies \: 6u + 8v = 1 \: \: \: \: ...(ii)eq$

Now subtract (ii) from (i) eq

$\rm \implies \: 6u + 24v - 6u - 8v = 5 - 1$

$\rm \implies \: 24v - 8v = 4$

$\rm \implies \: 16v = 4 \implies \: v = \dfrac{1}{4}$

Now put the value of v on (ii)eq

$\rm \implies \: 6u + 8v = 1 \: \: \: \: ...(ii)eq$

$\rm \implies \: 6u + 8 \times \dfrac{1}{4} = 1$

$\rm \implies \: 6u + 2 = 1$

$\rm \implies \: 6u = - 1$

$\rm \implies \: u = \dfrac{ - 1}{6}$

Now put the value of x and y on

$\rm \implies \: \dfrac{1}{x} = u \: \: and \: \: \dfrac{1}{y} = v$

$\rm \implies \: \dfrac{1}{x} = \dfrac{ - 1}{6} \: \: and \: \: \dfrac{1}{y} = \dfrac{1}{4}$

So we get

$\rm \implies \: x = - 6 \: \: and \: y = 4$