Year 10 - Maths
Solving a quadratic and linear pair of simultaneous equations using 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 (one linear, one quadratic) simultaneous equations algebraically using substitution.
Key Notes
- Consider which variable to make the subject for the substitution.
- Depending which variable you chose, you may need to expand a pair of bracketed expressions.
- Your choice may make the substitution significantly easier.
Vocabulary To Learn
- Substitution: Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.
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.
Consider which variable to make the subject for the substitution. Depending which variable you chose, you may need to expand a pair of bracketed expressions.
2. Use this key word in a maths sentence and explain it clearly. 'Substitution'
Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions. 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 elimination 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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