Systems of Equations Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Systems of Equations.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Two or more equations sharing the same variables, where the solution must satisfy all equations simultaneously.
Where two lines cross—the point that satisfies both equations.
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: The solution is where all constraints are satisfied simultaneously.
Common stuck point: Choose the right method: graphing, substitution, or elimination.
Sense of Study hint: Graph both equations on the same axes first to see roughly where the solution should be.
Worked Examples
Example 1
easySolution
- 1 Add the two equations to eliminate y: (x+y)+(x-y) = 10+4, giving 2x = 14.
- 2 Solve for x: x = 7.
- 3 Substitute back into x + y = 10: 7 + y = 10, so y = 3.
- 4 Check in second equation: 7 - 3 = 4 ✓
Answer
Example 2
mediumExample 3
hardPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.