Year 10 - Maths
Solving a quadratic and linear pair of simultaneous equations using 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 (one linear, one quadratic) simultaneous equations algebraically using elimination.
Key Notes
- When one equation is quadratic it will only be possible to eliminate the linear variable.
- Doing so produces a third equation which is quadratic.
- You can use any of your methods for solving a quadratic to find possible solutions.
- These values need to be substituted into one of the original equations to find its pair.
- If your quadratic has two valid solutions then you will have two pairs of solutions to your simultaneous equations.
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
- Pupils find the two $$x$$ values after solving the combined quadratic and declare that the solution.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When one equation is quadratic it will only be possible to eliminate the linear variable. Doing so produces a third equation which is quadratic.
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: Pupils find the two $$x$$ values after solving the combined quadratic and declare that the solution. Correction: It is important to substitute both $$x$$ values back in to one of the original equations to find the corresponding $$y$$ values. Without these, the solutions are incomplete.
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 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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