Year 10 - Maths
Solving algebraic simultaneous equations by elimination
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 solve two linear simultaneous equations algebraically using elimination.
Key Notes
- It is possible to find a solution that satisfies two equations with two unknowns by trial and error.
- A more efficient method is to combine the two equations to create a third valid equation .
- If the third equation contains only one unknown, it is easy to solve .
- Once you know one of the unknowns, you can substitute to find the other .
Vocabulary To Learn
- Simultaneous equations: Equations which represent different relationships between the same variables are called simultaneous equations.
- 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
- Performing different operations on different variables. E.g. subtracting one variable to eliminate then adding the other variable and constant. Pupils incorrectly think they are adding to eliminate.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
It is possible to find a solution that satisfies two equations with two unknowns by trial and error. A more efficient method is to combine the two equations to create a third valid equation .
2. Use this key word in a maths sentence and explain it clearly. 'Simultaneous equations'
Equations which represent different relationships between the same variables are called simultaneous equations. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Performing different operations on different variables. E.g. subtracting one variable to eliminate then adding the other variable and constant. Pupils incorrectly think they are adding to eliminate. Correction: This is caused by negative number skills. Subtracting two identical values always gives zero even if both are negative. If a term is the same in both equations, we subtract to eliminate. Clear working is crucial here.
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
- 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 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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