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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

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    $\begingroup$ en.wikipedia.org/wiki/Consistent_and_inconsistent_equations $\endgroup$
    – Alexey Burdin
    Commented Jul 12, 2020 at 16:17
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    $\begingroup$ They are linearly dependent. If they give contradictory results they are called "inconsistent". If they both give the exact same results they are called redundant. If they are linearly independent neither of these will happen. $\endgroup$
    – fleablood
    Commented Jul 12, 2020 at 17:39
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    $\begingroup$ The word is "inconsistent". $\endgroup$
    – littleO
    Commented Jul 12, 2020 at 19:34

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

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