Question

best answer will be marked as brainliest​

Answer 1

1.

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

$\red{\implies} 5(y - 2) + x - 1 = 2$

$\red{\implies} 5y - 10 + x - 1 = 2$

$\red{\implies} x + 5y = 13 - - - - (a)$

$\rule{10cm}{0.05cm}$

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

$\red{\implies} 6(y - 2) - 3(x - 1) = 1$

$\red{\implies} 6y - 12 - 3x + 3 = 1$

$- 3x + 6y = 10 - - - - - (b)$

$(a) \times 3\red{\implies} 3x + 15y = 39 - - - (c)$

$(b) + (c) \red{\implies} 21y = 49$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{\implies} y = \frac{7}{3}$

$x = 13 - \frac{35}{3}$

$x = \frac{4}{3}$

$\rule{10cm}{0.05cm}$

$\rule{10cm}{0.05cm}$

2.

$\frac{1}{3x + y} + \frac{1}{3x - y} = \frac{3}{4}$

$\red{\implies} 3x - y + 3x + y = \frac{3}{4}$

$\red{\implies} 6x = \frac{3}{4}$

$\red{\implies} x = \frac{1}{8}$

$\rule{10cm}{0.05cm}$

$\frac{1}{2(3x + y)} - \frac{1}{2(3x - y)} = \frac{ - 1}{8}$

$\red{\implies} 6x - 2y - 6x - 2y = \frac{ - 1}{8}$

$\red{\implies} - 4y = \frac{ - 1}{8}$

$\red{\implies} y = \frac{1}{32}$