Question

How to solve 6x+3y-6xy=0 and 2x+4y-5xy=0 by elimination method

Answer 1

6x+3y-6xy=0 Eq-1

2x+4y-5xy=0 Eq-2

Add both the equations

8x+7y-11xy=0

11xy=8x+7y Eq-3

Since both are equal,

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

4x-y-xy=0

xy=4x-y

Putting xy in Eq-3

11(4x-y)=8x+7y

44x-11y=8x+7y

36x-18y=0 Eq-4

Putting xy in Eq-2

2x+4y-5xy=0

2x+4y-5(4x-y)=0

2x+4y-20x+5y=0

9y-18x=0

y-2x=0

y=2x  

Putting y in Eq-4

36x-18(2x)=0

36x-36x=0 //Here we can see that x is also=1, because 36 times 1=36

x=0;x=1

y=0;y=2

Ans.x=0,y=0

x=1;y=2