Systems: Elimination
Add or subtract equations to cancel a variable.
Key idea
Add or subtract equations to cancel a variable.
In depth
Add or subtract equations (after scaling) so that one variable cancels. It works because adding equal quantities to both sides of an equation keeps it true.
Worked example
x + y = 7 and x − y = 1: add to get 2x = 8, so x = 4 and y = 3.
Real-world uses
- Working out ticket prices from totals for adults and children
- Balancing chemical equations
Common mistake
Subtracting only some terms or forgetting to multiply every term when scaling.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Systems: Elimination?
Add or subtract equations to cancel a variable. It is a topic at the intermediate level in Algebra.
Where is Systems: Elimination used in real life?
Real-world examples: Working out ticket prices from totals for adults and children; Balancing chemical equations.
What should I learn before Systems: Elimination?
Make sure you are comfortable with Systems: Substitution, the previous topic in Algebra.
What is a common mistake with Systems: Elimination?
Subtracting only some terms or forgetting to multiply every term when scaling.
How can I practise Systems: Elimination?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Systems: Elimination?
Move on to Systems with Three Variables next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.