Consistency Math Example 4

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

Example 4

medium
Is {x+y+z=1x+y+z=3\begin{cases} x + y + z = 1 \\ x + y + z = 3 \end{cases} consistent?

Solution

  1. 1
    Subtracting: 0=20 = 2. Contradiction.
  2. 2
    No, inconsistent. These are parallel planes that never intersect.

Answer

No, inconsistent.
The same left-hand side cannot equal two different constants. This extends the 2D parallel-lines test to 3D — parallel planes with different constants have no intersection.

About Consistency

A system of equations is consistent when there exists at least one set of variable values that satisfies every equation simultaneously.

Learn more about Consistency →

More Consistency Examples

Example 1 easy

Is the system [formula] consistent?

Example 2 medium

For what value of [formula] is [formula] consistent?

Example 3 easy

Is [formula] consistent?

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