Consistency (Meta) Math Example 2

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

Example 2

medium
Check whether the system of equations x+y=5x + y = 5 and 2x+2y=112x + 2y = 11 is consistent.

Solution

  1. 1
    From the first equation: y=5−xy = 5 - x. Substitute into the second: 2x+2(5−x)=112x + 2(5-x) = 11.
  2. 2
    Simplify: 2x+10−2x=112x + 10 - 2x = 11, giving 10=1110 = 11. This is a contradiction.
  3. 3
    The system is inconsistent — there is no solution.

Answer

Inconsistent — no solution exists\text{Inconsistent — no solution exists}
A system is inconsistent when its equations contradict each other. Geometrically, the two lines are parallel and never intersect. Detecting inconsistency prevents wasted computation.

About Consistency (Meta)

The property of a set of mathematical statements having no internal contradictions — all statements can be simultaneously true within the same system.

Learn more about Consistency (Meta) →

More Consistency (Meta) Examples

Example 1 easy

A student claims: 'The set [formula].' Check whether this definition is consistent.

Example 3 easy

A proof assumes both '[formula] is even' and '[formula] is odd'. Is this assumption consistent? What

Example 4 medium

Determine whether the conditions '[formula] is a prime number' and '[formula] is divisible by 4' are

← All Consistency (Meta) Examples Consistency (Meta) Concept