If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
For example, we have the system of linear equations:
[tex]\begin{gathered} y\text{ =3x + 2} \\ y\text{ - 3x = 0} \end{gathered}[/tex]When we attempt to solve the system:
Subtract equation 1 from 2:
[tex]\begin{gathered} y\text{ - 3x -y = 0 -(3x+2)} \\ -3x\text{ = -3x - 2} \\ \text{Collect like terms} \\ -3x\text{ + 3x = -2} \\ 0\text{ = -2} \end{gathered}[/tex]The result is false. Hence, there is no solution