How do I determine, if a system of linear equation is determined, underdetermined and incompatible?
2026-04-29 19:55:53.1777492553
system of linear equation: how to check if determined, underdetermined or incompatible?
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Are you asking whether a system
\begin{align} Ax + By &= C \\ Dx + Ey &= F \end{align}
has no, one, or infinitely many solutions?
Well, if that is the case, then think of the two (three, four, five etc.) equations as lines. If they are parallel (same slope) but have different $y-$intercepts, then they have no solutions; they will never intersect. If they are not parallel, then they have one solution (this works for two only. 3+ the equations have to be concurrent). If they have the same $y-$intercepts and the same slope, then they are the same line and so they have infinitely many solutions.