2x + 6y = 3 / * 2 ;
4x + 12y = 6 ;
We compare with 4x + 2my = 6 ;
If 12 = 2m ( m = 6 ), we have an infinite solution ;
If 12 isn't 2m ( m isn't 6 ), we have one solution ;
For example, m = 5 ( it isn't 6 ) ; we solve the system of equations ;
2x = 3 - 6y ;
4x = 6 - 12y;
( 6 - 12y ) + 2*5*y = 6;
6 - 12y + 10y = 6;
-2y = 0 ;
y = 0 ; x = 3 / 2;
In conclusion. there is no value of m for the system of equations has no solution !
