If 2x + 6y = 3xy and 10x -­ 3y = 4xy, find x, y.

Equation 1 : 2x + 6y = 3xy   

Equation 2 : 10x -­ 3y = 4xy   

Dividing both equations by $$(xy)$$

=> $$\frac{2}{y} + \frac{6}{x} = 3$$

and $$\frac{10}{y}-\frac{3}{x} = 4$$

Let $$\frac{1}{y} = u$$ and $$\frac{1}{x} = v$$

=> $$2u+6v=3$$ ------------(iii)

and $$10u-3v=4$$ ------------(iv)

Multiplying equation (iv) by 2 and adding it to equation (iii), we get :

=> $$22u = 11$$

=> $$u = \frac{11}{22} = \frac{1}{2}$$

Substituting it in equation (iii), => $$6v = 3 - 1 = 2$$

=> $$v = \frac{2}{6} = \frac{1}{3}$$

$$\therefore (x,y) = (3,2)$$

=> Ans - (A)