Answer
If one equation is the multiple of another equation (but with a different numerical value)--or if there is a false statement in the equation, then there is no solution.
Work Step by Step
Example:
$x+y+z=2$
$-x-y-z=1$
$3x-4y+z=56$
If we multiply the middle equation by $-1$, then we have $x+y+z=-1$. However, the first equation is $x+y+z=2$, so there are two equations with different numerical values. (Thus, there is no solution to the system.)
If we added the first two equations together, we would have $0=3$, which we know is false. (Thus, there is no solution to the system.)
