Year 10 - Maths
Combining 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 additively combine two equations to create a third valid equation.
Key Notes
- Two equations can be combined into a third equation.
- You can combine equations using the standard arithmetic operations.
- The new equation may not contain both variables any more.
Vocabulary To Learn
- 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
- Mistakes can be made when subtracting negative values. E.g. thinking that 5 - - 2 = 3.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Two equations can be combined into a third equation. You can combine equations using the standard arithmetic operations.
2. Use this key word in a maths sentence and explain it clearly. 'Elimination'
Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Mistakes can be made when subtracting negative values. E.g. thinking that 5 - - 2 = 3. Correction: Consider additive inverses, subtracting a negative is the same as adding the additive inverse. Pupils should be able to spot mistakes in learning cycle 1 by checking their new equation is still true.
More Lessons In This Unit
- Checking and securing understanding of interpreting graphs Study Guide
- Forming simultaneous equations Study Guide
- Problem solving with linear and quadratic simultaneous equations Study Guide
- Problem solving with 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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