Question

3/2x+2/3y=-1/3 and 3/4x+1/2y=-1/8

Answer 1

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Answer 2

$\frac{3}{2x} + \frac{2}{3y} = \frac{ - 1}{3} - - (1) \\ \\ \frac{3}{4x} + \frac{1}{2y} = \frac{ - 1}{8} - - (2)$

$from \: (1) \\ \\ \frac{3}{2x} + \frac{2}{3y} = \frac{ - 1}{3} \\ \\ = > \frac{9x + 4y}{6xy} = \frac{ - 1}{3} \\ \\ = > 3(9x + 4y) = - 1(6xy) \\ \\ = > 27x + 12y = - 6xy - - (3)$
$from \: (2) \\ \\ \frac{3}{4x} + \frac{1}{2y} = \frac{ - 1}{8} \\ \\ = > \frac{6x + 4y}{8xy} = \frac{ - 1}{8} \\ \\ = > 8(6x + 4y) = - 1(8xy) \\ \\ = > 48x + 32y = - 8xy - - (4)$
By Elimination method

$eqn(3) \: 27x + 12y = - 6xy \times48 \\ eqn(4) \: 48x + 32y = - 8xy \times 27\\ we \: get \\ \\ 1296x + 576y = - 288xy \\ 1296x + 864y = - 216xy \\ - - - - - - - - - - - - \\ \: \: \: \: 288y = - 72xy \\ \\ = > 288 = - 72 \\ \\ = > x = \frac{ - 288}{72} \\ \\ \\ = > x = - 4$
From eq'n ( 3 )

27x + 12y = - 6xy => 27x + 12y = - 6y

=> 27 ( - 4 ) + 12y = - 6( - 4 )y

=> - 108 + 12y = - 24y

=> 12y + 24y = - 108

=> 36y = - 108

=> y = - 3

=>

Therefore the value of x = - 4 and y = - 3