Question

find the value of x and y by cross multiplication method of 2/x-1 +3/y+1 =2, 3/x-1 + 2/y+1= 13/6​

Answer 1

Answer:

$1) \: \: \: \: \frac{2}{x - 1} + \frac{3}{y + 1} = 2 \\ \\ \frac{2(y + 1) + 3(x - 1)}{(x - 1)(y + 1)} = 2 \\ \\ \frac{2y + 2 + 3x - 3}{x(y + 1) - 1(y + 1)} = 2 \\ \\ \frac{3x + 2y - 3 + 2}{xy + x - y - 1} = 2 \\ \\ 3x + 2y - 1 = 2(xy + x - y - 1) \\ \\ 3x + 2y - 1 = 2xy + 2x - 2y - 2 \\ \\ 3x - 2x + 2y + 2y - 1 + 2 = 2xy \\ \\ x + 4y + 2 = 2xy....... \\ \\ \\ \\ 2) \: \: \: \frac{3}{x - 1} + \frac{2}{y + 1} = \frac{13}{6 } \\ \\ \frac{3(y + 1) + 2(x - 1)}{(x - 1)(y + 1)} = \frac{13}{6} \\ \\ \frac{3y + 3 + 2x - 2}{x(y + 1) - 1(y + 1)} = \frac{13}{6} \\ \\ \frac{2x + 3y + 3 - 2}{xy + x - y - 1} = \frac{13}{6} \\ \\ \frac{2x + 3y + 1}{xy + x - y - 1} = \frac{13}{6} \\ \\ 6(2x + 3y + 1) = 13(xy + x - y - 1) \\ \\ 12x + 18y + 6 = 13xy + 13x - 13y - 13 \\ \\ 12x - 13x + 18y + 13y + 6 + 13 = 13xy \\ \\ - x + 31y + 18 = 13xy.....$

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