Simultaneous Equations — Year 9 Revision Notes
These notes cover solving a pair of linear simultaneous equations by elimination and by substitution, and forming them from word problems — all at Year 9 (Stage 9) level.
Solving by elimination
To eliminate a variable, make its coefficients match, then add or subtract the equations. For x + y = 7 and x − y = 1, adding gives 2x = 8, so x = 4; substituting back gives y = 3. Add when the matching terms have opposite signs, subtract when they have the same sign.
Key Facts & Formulas
- Add or subtract to eliminate one unknown
- x + y = 7, x − y = 1 → x = 4, y = 3
Tips
- Make one pair of coefficients equal first if needed.
- Same signs subtract, opposite signs add.
Solving by substitution
Rearrange one equation to make a variable the subject, then substitute it into the other. For y = 2x and x + y = 9, substitute to get x + 2x = 9, so 3x = 9 and x = 3, then y = 6. Substitution works well when one variable is already on its own.
Key Facts & Formulas
- Substitute one equation into the other
- y = 2x, x + y = 9 → x = 3, y = 6
Tips
- Use substitution when one variable is already the subject.
- Replace the variable, do not just write it twice.
Checking and word problems
Always check your solution by substituting both values into both original equations. Many problems are written in words — define your unknowns with letters, form two equations, then solve. For example, '3 pens and 2 pencils cost $7' becomes 3p + 2c = 7.
Key Facts & Formulas
- Check in both equations
- Form two equations from the information
Tips
- Substitute your answer into both equations to check.
- Define your letters clearly in a word problem.
Revision Checklist
- I understand what simultaneous equations represent
- I can solve simultaneous equations by elimination
- I can solve simultaneous equations by substitution
- I can form and solve simultaneous equations from a word problem
Frequently Asked Questions
How can I check my answer is right?
Substitute both values back into both original equations. If each equation balances, your solution is correct. Checking only one equation is not enough, because a wrong pair can still satisfy a single equation.
Build strong foundations in Simultaneous Equations
A free trial class with Teacher Rig helps your Year 9 child master Simultaneous Equations now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Simultaneous Equations develops in IGCSE Algebra and Graphs (Cambridge 0580) →