Redundancy Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is y=2x+1y = 2x + 1 redundant in {y=2x+1y=−x+4\begin{cases} y = 2x + 1 \\ y = -x + 4 \end{cases}?

Solution

  1. 1
    No — the two equations have different slopes (2 vs −1-1).
  2. 2
    Neither is a multiple of the other. Both are independent.

Answer

No, both are independent.
Two equations with different slopes represent different lines. Neither can be derived from the other, so both provide unique constraints and are independent.

About Redundancy

An equation in a system that is a linear combination of the others and therefore adds no new constraints or information.

Learn more about Redundancy →

More Redundancy Examples

Example 1 easy

In [formula], is the second equation redundant?

Example 2 medium

In [formula], is equation 3 redundant?

Example 4 medium

If a [formula] system has rank 2, how many redundant equations are there?

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