Question

6 by x minus 1 minus 3 by y minus 2 is equal to 3 and


5 by x minus 1 + 1 by y minus 2 is equal to 2 give the solution​

Answer 1

Answer:

$\frac{6}{x - 1} - \frac{3}{y - 2} = 3....(1) \\ \frac{5}{x - 1} + \frac{1}{y - 2} = 2....(2) \\ multiplying \: equation \: (2) \: by \: 3 \: \\ and \: adding \: with \: equation \: (1) \\ \frac{6}{x - 1} - \frac{3}{y - 2} = 3 \\ \frac{15}{x - 1} + \frac{3}{y - 2} = 6 \\ - - - - - - - - - \\ \frac{6 + 15}{x - 1} = 9 \\ \implies \: x - 1 = \frac{21}{9} \\ \implies \: x - 1 = \frac{7}{3} \\ \implies \: x = \frac{7}{3} + 1 \\ \implies \: x = \frac{7 + 3}{3} \\ \huge \fbox {\implies \: x = \frac{10}{3}} \\ substituting \: x - 1 = \frac{7}{3} \: in \: equation \: (1) \\ \frac{6}{ \frac{7}{3}} - \frac{3}{y - 2} = 3 \\ \frac{6 \times 3}{7} - \frac{3}{y - 2} = 3 \\ \frac{6}{7} - \frac{1}{y - 2} = 1 \\ \frac{6}{7} - 1 = \frac{1}{y - 2} \\ \frac{6 - 7}{7} = \frac{1}{y - 2} \\ - \frac{1}{7} = \frac{1}{y - 2} \\ - 7 = y - 2 \\ 2 - 7 = y \\\huge \fbox {\implies \: y = - 5}$

Answer 2

I hope it may help you.