Question

solve for x and y---this equation☝️☝️​

Answer 1

$let \: \: \frac{1}{x - 1} = a \: and \: \frac{1}{y - 2} = b \\ \\ 5a - b = 2 - - - - 1 \times 3 \\ 6a - 3b = 1 - - - -2 \\ \\ 15a -3 b = 6 \\ \: 6a - 3b = 1 \\ - - - - - - - \\ 21a \: \: \: \: \: = 7 \\ \\ a = \frac{7}{21} = \frac{1}{3} \\ \\ \frac{1}{x - 1} = a = \frac{1}{3} \\ \\ x - 1 = 3 \\ x = 4 \\ \\ substitute \: eq - a \: in \: eq - 1 \\ \\ 5a - b = 2 \\ \\ 5( \frac{1}{3} ) - b = 2 \\ \\ \frac{5}{3} - b = 2 \\ \\ 5 - 3b= 6\\ \\ - 3b = 1 \\ \\ b = \frac{ - 1}{3} \\ \\ \frac{1}{y - 2} = b = \frac{ - 1}{3} \\ \\ 3 = - y + 2 \\ \\ y = - 1 \\ \\ therefore \: \\ x = 4 \\ y = - 1$

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Answer 2

Given :

$\frac{5}{x-1}-\frac{1}{y-2}=2\\\\\frac{6}{x-1}-\frac{3}{y-2}=1$

Explanation:

let

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

thus the equations become

5u -v = 2 ..(1)

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

multiply equation 1 by 3 we get

15 u - 3v = 6 ...(3)

now solving 1 and 3 by elimination method we get

u = $\frac{5}{9}$

put the value of u in equation 1 we get

$5u -v = 2\\\\5 (\frac{5}{9}) -v = 2 \\\\ \frac{25}{9}-v = 2\\\\v = \frac{25}{9}-2 \\\\v = \frac{25-18}{9} \\\\v = \frac{6}{9}= \frac{2}{3}$

now ,

$\frac{1}{x-1}= u \\\\\frac{1}{x-1}=\frac{5}{9}\\\\9 = 5(x-1)\\\\9 = 5x-5\\\\14=5x\\\\x=\frac{14}{5}$

$\frac{1}{y-2} = v \\\\ \frac{1}{y-2} =\frac{2}{3}\\\\3 = 2(y-2)\\\\3 = 2y-4\\\\7=2y\\\\y = \frac{7}{2}$

thus , The value of x and y are 14/5 and 7/2

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https://brainly.in/question/3753504