Question

Solve for x and y,
5/x-1 +1/y-2=2 and 6/x-1 -3/y-2=1

Answer 1

Answer:

advert is 6

I hope this will help you

Answer 2

Answer

$\sf \dashrightarrow \dfrac{5}{x - 1} + \dfrac{1}{y - 2} = 2 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{6}{x - 1} + \dfrac{-3}{y - 2} = 1 \: \: --- (ii)$

Let $\sf \dfrac{1}{x - 1}$ be u.

Let $\sf \dfrac{1}{y - 2}$ be v.

So, the equations become

$\sf \dashrightarrow 5u + v = 2$

$\sf \dashrightarrow 6u - 3v = 1$

By first equation,

$\sf \dashrightarrow 5u + v = 2$

$\sf \dashrightarrow 5u = 2 - v$

$\sf \dashrightarrow u = \dfrac{2 - v}{5}$

Now, we should find the value of y by second equation.

$\sf \dashrightarrow 6u - 3v = 1$

$\sf \dashrightarrow 6 \bigg( \dfrac{2 - v}{5} \bigg) - 3v = 1$

$\sf \dashrightarrow \dfrac{12 - 6v}{5} - 3v = 1$

$\sf \dashrightarrow \dfrac{12 - 6v - 15v}{5} = 1$

$\sf \dashrightarrow \dfrac{12 - 21v}{5} = 1$

$\sf \dashrightarrow 12 - 21v = 5$

$\sf \dashrightarrow -21v = 5 - 12$

$\sf \dashrightarrow -21v = -7$

$\sf \dashrightarrow v = \dfrac{-7}{-21}$

$\sf \dashrightarrow v = \dfrac{1}{3}$

Now, we can find the value of u by first equation.

$\sf \dashrightarrow 5u + v = 2$

$\sf \dashrightarrow 5u + \dfrac{1}{3} = 2$

$\sf \dashrightarrow \dfrac{15u + 1}{3} = 2$

$\sf \dashrightarrow 15u + 1 = 3 \times 2$

$\sf \dashrightarrow 15u + 1 = 6$

$\sf \dashrightarrow 15u = 6 - 1$

$\sf \dashrightarrow 15u = 5$

$\sf \dashrightarrow u = \dfrac{5}{15}$

$\sf \dashrightarrow u = \dfrac{1}{3}$

Now, we can find the values of x and y.

We know that,

$\sf \dashrightarrow \dfrac{1}{x - 1} = u$

$\sf \dashrightarrow \dfrac{1}{x - 1} = \dfrac{1}{3}$

$\sf \dashrightarrow 3 = 1 (x - 1)$

$\sf \dashrightarrow 3 = x - 1$

$\sf \dashrightarrow x = 3 + 1$

$\sf \dashrightarrow x = 4$

We also know that,

$\sf \dashrightarrow \dfrac{1}{y - 2} = v$

$\sf \dashrightarrow \dfrac{1}{y - 2} = \dfrac{1}{3}$

$\sf \dashrightarrow 3 = 1 (y - 2)$

$\sf \dashrightarrow 3 = y - 2$

$\sf \dashrightarrow y = 3 + 2$

$\sf \dashrightarrow y = 5$

Hence, the values of x and y are 4 and 5 respectively.