Question

solve the following pairs of equation by reducing them to a pair of linear equations:
1) 5/x-1 + 1/y-2=2
6/x-1 + 3/y-2=1​

Answer 1

$\huge\mathcal{Answer:}$

Let:-

$\frac{1}{x - 1} = u$

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

so our equation become

$5u + v = 2 - - - - (1)$

$6u - 3v = 1 - - - (2)$

from (1)

$5u + v = 2$

$v = 2 - 5v$

putting value of v in(2)

$6u - 3v = 1$

$6u - 3(2 - 5v) = 1$

$6u - 6 + 15v = 1$

$6u + 15v = 1 + 6$

$21u = 7$

$u = \frac{7}{21}$

$u = \frac{1}{3}$

$putting \: u = \frac{1}{3} in \: eq(1)$

$5u + v = 2$

$5( \frac{1}{3} ) + v = 2$

$\frac{5}{3} + v = 2$

$v = 2 - \frac{5}{3}$

$v = \frac{2(3) - 5}{3}$

$v = \frac{6 - 5}{3}$

$v = \frac{1}{3}$

$hence \: u = \frac{1}{3} v = \frac{1}{3}$

but we need to find x and y

$u = \frac{1}{x - 1}$

$\frac{1}{ 3} = \frac{1}{x - 1}$

$x - 1 = 3$

$x = 3 + 1$

$x = 4$

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

$\frac{1}{3} = \frac{1}{y - 2}$

$y - 2 = 3$

$y = 3 + 2$

$y = 5$

$hence \: x = 4 \: \: y = 5$