Redundancy Math Example 1

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

Example 1

easy
In {x+y=32x+2y=6\begin{cases} x + y = 3 \\ 2x + 2y = 6 \end{cases}, is the second equation redundant?

Solution

  1. 1
    Step 1: Divide equation 2 by 2: x+y=3x + y = 3.
  2. 2
    Step 2: This is identical to equation 1.
  3. 3
    Step 3: Yes, equation 2 adds no new information โ€” it is redundant.

Answer

Yes, equation 2 is redundant.
A redundant equation is a scalar multiple of another equation (or a linear combination of other equations). It doesn't reduce degrees of freedom or constrain the solution further.

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 โ†’

More Redundancy Examples