Question

solve the following pairs of linear equations. 2/x + 2/3y = 1/6. 2/x - 1/y =1​

Answer 1

Answer:

x=4 and y=-2

Step-by-step explanation:

we have....

$\frac{2}{x} + \frac{2}{3y} = \frac{1}{6}$

and

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

let

$\frac{1}{x} = a$

and

$\frac{1}{y} = b$

then.. we get.

$2a + \frac{2b}{3} = \frac{1}{6} ...........(1)$

and....

$2a - b = 1$

$2a = 1 + b$

putting this value in eq 1.. we get..

$1 + b + \frac{2b}{3} = \frac{1}{6}$

therefore we get

$b = \frac{ - 1}{2}$

put this b again..

$a = \frac{1}{4}$

as we took.

$\frac{1}{x} = a \: \: \: \: and \: \: \: \: \frac{1}{y} = b$

then

$\frac{1}{4} = \frac{1}{x} \: \: \: and \: \: \: \: \frac{ - 1}{2} = \frac{1}{y}$

therefore...

$x = 4 \: \: \: \: \: \: and \: \: \: \: y = - 2$

hope it helps...