Consistency Math Example 1

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

Example 1

easy
Is the system {x+y=52x+2y=8\begin{cases} x + y = 5 \\ 2x + 2y = 8 \end{cases} consistent?

Solution

  1. 1
    Step 1: Simplify equation 2: x+y=4x + y = 4.
  2. 2
    Step 2: Compare: x+y=5x + y = 5 and x+y=4x + y = 4. Contradiction!
  3. 3
    Step 3: No values of x,yx, y satisfy both. The system is inconsistent.

Answer

Inconsistent (no solution)
A system is consistent if at least one solution exists. Here the two equations demand x+yx + y equal both 5 and 4 simultaneously, which is impossible.

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 2 medium

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

Example 3 easy

Is [formula] consistent?

Example 4 medium

Is [formula] consistent?

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