Year 10 - Maths
Solving simultaneous linear equations by substitution
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 substitution.
Key Notes
- You can use your knowledge of changing the subject to rewrite one or both equations.
- If one of the variables is the subject, the equivalent expression can be substituted into the other equation.
- This is another method that involves reducing the number of variables.
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.
- Substitution: Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values, terms, or expressions.
- Subject (equation/formula): The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1
Common Mistakes To Avoid
- Incorrectly expanding brackets or not using brackets when one expression is substituted into another.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
You can use your knowledge of changing the subject to rewrite one or both equations. If one of the variables is the subject, the equivalent expression can be substituted into the other equation.
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: Incorrectly expanding brackets or not using brackets when one expression is substituted into another. Correction: Pupils should always use brackets when substituting. Remind them of the distributive law and that multiplying a negative value by a negative value gives a positive value. Checking final answers should catch these mistakes.
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 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 graphically Study Guide
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