Year 10 - Maths
Solving more complex 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 complex linear simultaneous equations algebraically using elimination.
Key Notes
- Additively combining the equations does not eliminate one variable unless the coefficients are the same.
- Equivalent equations should be formed so the coefficients of one variable are the same (if not already).
- When considering the coefficients, use your knowledge of LCM to help.
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
- Forgetting to multiply every term in the equation when scaling or not multiplying every term by the same value.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Additively combining the equations does not eliminate one variable unless the coefficients are the same. Equivalent equations should be formed so the coefficients of one variable are the same (if not already).
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: Forgetting to multiply every term in the equation when scaling or not multiplying every term by the same value. Correction: Remind pupils that in order to maintain equality, the entire expression on both sides of the equals sign must be multiplied by the same value. Clear working and checking solutions can help pupils spot when they have made this mistake.
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 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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