Video: The Relation between the Number of Equations and the Numbers of Variables in a System of Equations

Suppose a system of equations has fewer equations than variables. Must such a system be consistent?

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Video Transcript

Suppose a system of equations has fewer equations than variables. Must such a system be consistent?

For a system to be consistent, there must be at least one set of values for the unknowns that satisfies every equation in the system. That’s another way of saying they have at least one solution. But if we have more variables than equations, we can’t solve for every variable. And if we can’t solve for every variable, then we can’t prove it’s a consistent system.

So no, if we have fewer equations than variables, the system might not be consistent. In order to solve, we need at least as many equations as there are variables.

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