Is there a word for a contradictory set of linear system of equations?

Question

So in basic math, we tend to learn that we can solve for the variables if there are n equations and n unknowns. But let's say the equations are contradictory, for example, $x + y = 1$ and $x + y = 5$.

Is there an official math word for a contradictory set of equations so that you can't solve it?

Thanks

Answer 1

They are called inconsistent equations, as the set of variables that would solve the first equation $x+y=1$ would not solve the second $x+y=5$.