Simultaneous equations for Singapore O-Level G3 Math
Choose elimination when coefficients match or cancel easily; choose substitution when one variable is already isolated. Both methods find the pair that satisfies both equations. Compare them on the same example below, then check the answer in each original equation.
What this guide covers
Simultaneous linear equations in two unknowns by elimination, substitution and graphical interpretation. This guide teaches the two algebraic methods and explains the intersection meaning.
Syllabus reference: 2026 Mathematics 4052, N7, page 7. These are Mentora search groupings, not new official syllabus categories.
The content in this guide was also checked against 2027 G3 Mathematics K310, N7, page 7 on 2026-09-12. This is subject-content alignment, not a claim of complete syllabus coverage.
Use this guide for revision
What questions usually test
- Solve two linear equations by elimination or substitution.
- Translate a short context into two equations with defined unknowns.
- Interpret a solution as the values that satisfy both equations or their graph intersection.
How to revise simultaneous equations
Step 1
Define both unknowns
For a word problem, state what each variable represents and use consistent units.
Step 2
Choose the shorter route
Eliminate matching coefficients or substitute an already isolated variable.
Step 3
Check both equations
Substitute the pair into each original equation before interpreting the answer.
When should I use elimination or substitution for simultaneous equations?
- Elimination
- Choose it when one pair of coefficients already matches or becomes equal with one small multiplication. Add or subtract the complete equations to remove that unknown.
- Substitution
- Choose it when an equation already says x = … or y = …, or when a coefficient of 1 makes one unknown easy to isolate. Substitute the whole expression, including its signs.
- Exam choice
- Scan both equations before calculating and choose the route with fewer operations. If one route creates awkward tions or extra expansion, the other valid method is usually quicker.
Worked example
Solve 2x + y = 11 and x − y = 1 by elimination.
Add the equations: 3x = 12, so x = 4. Substitute into x − y = 1 to get y = 3. Check both: 2(4) + 3 = 11 and 4 − 3 = 1.
Substitution on the same pair
Now solve 2x + y = 11 and x − y = 1 by substitution.
From x − y = 1, write y = x − 1. Substitute the whole expression: 2x + (x − 1) = 11. Then 3x = 12, x = 4 and y = 3. Both methods give the same intersection (4, 3). Elimination is shorter here because +y and −y already cancel; substitution is equally valid.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Solve x + y = 9 and x − y = 3.
Show worked answer
Add to give 2x = 12, so x = 6 and y = 3. Both 6 + 3 = 9 and 6 − 3 = 3 check.
Check 2
Solve y = 2x + 1 and 3x + y = 16.
Show worked answer
Substitute: 3x + 2x + 1 = 16, so x = 3 and y = 7. Check 9 + 7 = 16.
Check 3
Two notebooks and one pen cost $12. One notebook and two pens cost $9. Find each price.
Show worked answer
Let n and p be prices in dollars. 2n + p = 12 and n + 2p = 9. Double the first equation and subtract the second: 3n = 15, so n = 5 and p = 2. Check both equations independently: 2(5) + 2 = 12 and 5 + 2(2) = 9.
Common mistakes to watch for
- Multiplying an equation means multiplying every term and the right-hand side.
- Subtract the entire second equation, including negative terms.
- One equation alone is not enough to verify a pair of unknowns; substitute into both.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
You may need first
These verified prerequisite links suggest useful foundations. They do not make a claim about your current readiness.
- Linear equations in one variableAfter eliminating one unknown, solve the remaining one-variable equation before substituting back.Practise simultaneous equations →
- Linear functions and their graphsFor the graphical method, the common solution is the intersection of two lines. Read both coordinates.Practise functions and graphs →
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Published by Mentora · Sources checked 12 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.