If 7x + 6y = 5xy and 10x - 4y = 4xy, then value of x and y is

Equation 1 : 7x + 6y = 5xy   

Equation 2 : 10x -­ 4y = 4xy   

Dividing both equations by $$(xy)$$

=> $$\frac{7}{y} + \frac{6}{x} = 5$$

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

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

=> $$7u+6v=5$$ ------------(iii)

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

Multiplying equation (iv) by 3 and equation (iii) by 2 and adding them, we get :

=> $$(14u+30u) = (10+12)$$

=> $$u = \frac{22}{44} = \frac{1}{2}$$

Substituting it in equation (iv), => $$4v = 5 - 4 = 1$$

=> $$v = \frac{1}{4}$$

$$\therefore (x,y) = (4,2)$$

=> Ans - (C)