Consistency Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Consistency.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A system of equations is consistent when there exists at least one set of variable values that satisfies every equation simultaneously.
The constraints don't contradict each other—there's some answer that works.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Consistent means 'solvable'; inconsistent means 'no solution exists.'
Common stuck point: Inconsistency often shows as 0 = 5 or similar contradiction.
Sense of Study hint: Simplify the system fully. If you reach a statement like 0 = 5, stop and declare no solution exists.
Worked Examples
Example 1
easySolution
- 1 Step 1: Simplify equation 2: x + y = 4.
- 2 Step 2: Compare: x + y = 5 and x + y = 4. Contradiction!
- 3 Step 3: No values of x, y satisfy both. The system is inconsistent.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.