Question

6x+3y=6xy or 2x+4y=5xy

Answer 1

1st Equation : 6x + 3y = 6xy  --------------- (1)

2nd Equation : 2x + 4y = 5xy  -------------- (2)

On solving (1) & (2) * 3, we get

6x + 12y = 15xy

6x + 3y = 6xy

-------------------------
 
        9y = 9xy

         x = 1.


Substitute x = 1 in (1), we get

6x + 3y = 6xy

6(1) + 3y = 6(1)(y)

6 + 3y = 6y

6 = 6y - 3y

6 = 3y

y = 2.


Therefore x = 1 and y = 2.



Hope this helps!

Answer 2

Solution :

Given equations are,

6x+3y=6xy _____(1)

2x+4y=5xy _____(2)

From eq (1) and (2) ×3

We get,


$\: \: 6x + 3y = 6xy \\ \: \: 6x + 12y = 15xy \\ - \: \: \: \: - \: \: \: \: \: \: \: \: \: \: - \\ - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 9y = 9xy$
9y-9xy = 0

9y(1-x) = 0

y(1-x) = 0

=> y = 0 or x = 1

1) If y = 0,

From (i) we get,

6x+3(0) = 6x(0)

6x = 0

=> x = 0

2) If x = 1

From (i) we get,

6(1)+3y = 6(1)y

=> 6 = 6y-3y

=> 3y = 6

=> y = 2

Hence,

x = 0 , y = 0
OR
x = 1 , y = 2