Question

solve
5/x-1 + 1/y-2=2
6/x-1 + -3/y-2=1​

Answer 1

Answer:

□X=4✔✔

□Y=5✔✔

Step-by-step explanation:

$\frac{5}{x - 1} + \frac{1}{y - 2} = 2 - - - - - (1) \\ \frac{6}{x - 1} + \frac{ - 3}{y - 2} = 1 - - - - - (2) \\ let \: \frac{1}{x - 1} = p - - - - - (3) \\ \: \: \: \: \: \frac{1}{x - 2} = q - - - - - (4) \\ putting \: value \: of \: (3) \: and \: (4) \: in \: (1) \: and \: (2) \: so \: we \: get \: \\ 5p + q = 2 \\ 5p = 2 - q \\ p = \frac{2 - q}{5} - - - - - - (5) \\ again \\ 6p - 3q = 1 \\ putting \: value \: of \: p \: \\ 6 \times (\frac{2 - q}{5}) - 3q = 1 \\ \frac{12 - 6q - 15q}{5} = 1 \\ - 21q = 5 - 12 \\ q = \frac{ - 7}{ - 21} \\ q = \frac{1}{3} \\ putting \: value \: of \: q \: in \: (5) \\5 p = 2 - \frac{1}{3} \\ 5p = \frac{5}{3} \\ p = \frac{1}{3} \\ putting \: value \: of \: p \: and \: q \: in \: (3) \: and \: (4) \: we \: get \\ \frac{1}{x - 1} = \frac{1}{3} \\ x = 4 \\ again \\ \frac{1}{y - 2} = \frac{1}{3} \\ y = 5$