Question

solve the following 2x +3y =4xy, 3x + y= 10 xy​

Answer 1

SOLUTION :-

$2x + 3y = 4xy = > x = \frac{4xy - 3y}{2} - eq(1) \\ \\ 3x + y = 10xy = > x = \frac{10xy - y}{3} - eq(2) \\ \\ since \: lhs \: is \: equal \: rhs \: can \: be \: equated \\ \\ = > \frac{4xy - 3y}{2} = \frac{10xy - y}{3} \\ \\ = > 3(4xy - 3y) = 2(10xy - y) \\ \\ = > 12xy - 9y = 20xy - 2y \\ \\ = > - 7y = 8xy \\ \\ = > 0 = 8xy + 7y \\ \\ = > 0 = y(8x + 7) \\ \\ = > 8x + 7 = 0 \\ \\ = > \frac{ - 7}{8} = x \\ \\ from \: eq(1) \\ \\ \frac{ - 7}{8} = \frac{4xy - 3y}{2} \\ \\ = > \frac{ - 7}{4} = 4xy - 3y \\ \\ = > \frac{ - 7}{4} = y(4x - 3) \\ \\ = > \frac{ - 7}{4} = y(4 \times \frac{ - 7}{8} - 3) \\ \\ = > \frac{ - 7}{4} = y( \frac{ - 7}{2} - 3) \\ \\ = > \frac{ - 7}{4y} = ( \frac{ - 13}{2} ) \\ \\ = > \frac{ - 7}{2y} = - 13 \\ \\ = > - 7 = - 26y \\ \\ = > y = \frac{7}{26}$