Question

9x + 5y = 37xy ; 7x - 4y = 13 xy

Answer 1

$9x + 5y = 37xy \\ \frac{9x + 5y}{xy} = 37 \\ \frac{9x}{xy} + \frac{5y}{xy} = 37 \\ 9y + 5x = 37 \: \: - - - - (i) \\ \\ 7x - 4y = 13xy \\ \frac{7x - 4y}{xy} = 13 \\ \frac{7x}{xy} - \frac{4y}{xy} = 13 \\ 7y - 4x = 13 \: \: - - - - -(ii) \\ \\ \\ multiply \: eq.(i) \: by \: 4 \: and \: eq.(ii) \: by \: 5$

36y + 20x = 148
35y - 20x = 65
---------------------------
71x = 213
---------------------------

x = 213/71 = 3

7y - 4x = 13

7y - 12 = 13

7y = 35

y = 35/7 = 5

So,

x = 3 and y = 5