Year 10 - Maths
Problem solving with simultaneous equations
Simultaneous equations: 2 variables
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.
Lesson Summary
You will learn to use your knowledge of simultaneous equations to solve problems.
Key Notes
- Where a problem gives multiple ways of connecting two things, it may mean simultaneous equations can be written.
- If simultaneous equations can be written, it is important to state what each variable stands for.
- The solutions should always be given in context.
Vocabulary To Learn
- Substitution: Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.
- Elimination: Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.
Common Mistakes To Avoid
- Simultaneous equations cannot be applied usefully to real-world scenarios.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Where a problem gives multiple ways of connecting two things, it may mean simultaneous equations can be written. If simultaneous equations can be written, it is important to state what each variable stands for.
2. Use this key word in a maths sentence and explain it clearly. 'Substitution'
Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Simultaneous equations cannot be applied usefully to real-world scenarios. Correction: The skill of solving a pair of simultaneous equations can be applied to a wide variety of problems and provides us with answers in a wide variety of contexts.
More Lessons In This Unit
- Checking and securing understanding of interpreting graphs Study Guide
- Combining equations Study Guide
- Forming simultaneous equations Study Guide
- Problem solving with linear and quadratic simultaneous equations Study Guide
- Solving a quadratic and linear pair of simultaneous equations graphically Study Guide
- Solving a quadratic and linear pair of simultaneous equations using elimination Study Guide
- Solving a quadratic and linear pair of simultaneous equations using substitution Study Guide
- Solving algebraic simultaneous equations by elimination Study Guide
- Solving more complex simultaneous equations by elimination Study Guide
- Solving simultaneous equations by elimination from a context Study Guide
- Solving simultaneous equations via any method Study Guide
- Solving simultaneous linear equations by substitution Study Guide
- Solving simultaneous linear equations graphically Study Guide
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