Systems: Substitution
Solve one equation for a variable and substitute into the other.
Key idea
Solve one equation for a variable and substitute into the other.
In depth
Solve one equation for a variable, then substitute that expression into the other equation. This turns two unknowns into one, which you can solve.
Worked example
y = 2x and x + y = 9: x + 2x = 9, x = 3, y = 6.
Real-world uses
- Solving mixture problems such as blending two coffees to a target price per kilo
Common mistake
Substituting back into the same equation you solved, which gives nothing new.
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: Substitution?
Solve one equation for a variable and substitute into the other. It is a topic at the intermediate level in Algebra.
Where is Systems: Substitution used in real life?
Real-world examples: Solving mixture problems such as blending two coffees to a target price per kilo.
What should I learn before Systems: Substitution?
Make sure you are comfortable with Systems of Equations: Graphing, the previous topic in Algebra.
What is a common mistake with Systems: Substitution?
Substituting back into the same equation you solved, which gives nothing new.
How can I practise Systems: Substitution?
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: Substitution?
Move on to Systems: Elimination 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”.