One solution: The result is a solution for one variable.
No solution: The result is a false statement.
Infinitely many solutions: The result is an identity.
We are told that we got 0=4 after adding two linear equations in a system. This is a contradiction because 0 is not equal to 4. Therefore, we can conclude that such system of equations has no solution.
Extra
Example
To make sense of the explanation, let's consider an example system that will result in 0=4 when we add the equations in the system.
2x-y= 3 & (I) y-2x= 1 & (II)
We will add these equations.
2x-y+ y-2x= 3+ 1
⇓
0=4
We arrived at a contradiction because 0 is not equal to 4. This means that there is no a common point satisfying both equations. Therefore, the lines that represent the equations are parallel, and there is no solution to the system. Let's look at the graph of the system to visualize it.
