Redundancy Math Example 2

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

Example 2

medium
In {x+y=22x−y=13x=3\begin{cases} x + y = 2 \\ 2x - y = 1 \\ 3x = 3 \end{cases}, is equation 3 redundant?

Solution

  1. 1
    Step 1: Add equations 1 and 2: (x+y)+(2x−y)=2+1(x+y) + (2x-y) = 2 + 1, giving 3x=33x = 3.
  2. 2
    Step 2: Equation 3 is the sum of equations 1 and 2.
  3. 3
    Step 3: Yes, it's redundant — it's a linear combination of the others.

Answer

Yes, equation 3 is redundant.
Redundancy isn't limited to scalar multiples. Any equation that can be derived as a linear combination of other equations in the system is redundant and doesn't provide new constraints.

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 3 easy

Is [formula] redundant in [formula]?

Example 4 medium

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

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