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S3 Maths: Simultaneous Linear Equations by Elimination (Paper 1 (basics))
S3 Maths: Simultaneous Linear Equations by Elimination (Paper 1 (basics))
Paper 1 (basics): ten simultaneous-equation questions with answers and one-line notes.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Simultaneous Linear Equations by Elimination |
| Level | S3 |
02 Questions (10 items)
- FoundationSolve x + y = 10 and x – y = 2.
- FoundationSolve x + y = 7 and x – y = 1.
- FoundationSolve 2x + y = 11 with y = 3.
- IntermediateSolve 3x + 2y = 12 with x = 2.
- IntermediateSolve 5x + 2y = 16 and 3x + 2y = 12.
- IntermediateSolve 4x + 3y = 18 and 4x – 3y = 6.
- ChallengeSolve 3x + 2y = 16 and 3x – 2y = 8.
- ChallengeSolve 5x + 3y = 31 and 2x + 3y = 16.
- ChallengeSolve x + 2y = 11 and 3x – 2y = 9.
- Error redoA student solves x + y = 8 and x – y = 2 by subtracting and gets 2y = 10, answering y = 5. What went wrong and what is the correct answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 6, y = 4 | Adding the two equations cancels y and gives 2x = 12; substituting back gives y = 4. |
| 2 | x = 4, y = 3 | Adding gives 2x = 8 so x = 4, and substituting back gives y = 3. |
| 3 | x = 4, y = 3 | With y equal to 3, substitution gives 2x = 8, so x = 4. |
| 4 | x = 2, y = 3 | Substituting x = 2 gives 6 + 2y = 12, so 2y = 6 and y = 3. |
| 5 | x = 2, y = 3 | The y terms are the same, so subtracting gives 2x = 4 and back substitution gives 2y = 6. |
| 6 | x = 3, y = 2 | Adding removes y to give 8x = 24, so x = 3 and then 3y = 6. |
| 7 | x = 4, y = 2 | Adding gives 6x = 24 so x = 4, and substituting back gives 2y = 4. |
| 8 | x = 5, y = 2 | Subtracting removes y to give 3x = 15, so x = 5 and then 3y = 6. |
| 9 | x = 5, y = 3 | Adding gives 4x = 20 so x = 5, and then 2y = 6 gives y = 3. |
| 10 | Subtracting leaves -2y = 6; the correct answer is x = 5, y = 3 | Check which unknown has equal or opposite coefficients: x is the same in both, so adding gives 2x = 10. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
The first step in elimination is always alignment: put the same unknown in the same column and the constant on the right. If one unknown has equal or opposite coefficients, add or subtract straight away; if the coefficients differ, multiply a whole equation through, every term including the right-hand side. Once one unknown is found, substitute it into either original equation for the other, then check both values in both equations.Tutor Registration →
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