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S3 Maths: Simultaneous Linear Equations by Elimination (Paper 2 (intermediate))
S3 Maths: Simultaneous Linear Equations by Elimination (Paper 2 (intermediate))
Paper 2 (intermediate): 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 2x + 3y = 12 and 2x + y = 8.
- FoundationSolve 3x + 4y = 25 and 3x + y = 13.
- FoundationSolve 5x + 4y = 32 and 5x – 4y = 8.
- IntermediateSolve 3x + 2y = 19 and 2x + 2y = 14.
- IntermediateSolve x + y = 9 and 2x + 3y = 22.
- IntermediateSolve 2x + y = 13 and x + 3y = 19.
- ChallengeSolve 2x + 3y = 17 and 5x – 3y = 11.
- ChallengeSolve 2x + 3y = 18 and 5x – 2y = 7.
- ChallengeTwo numbers add to 45 and differ by 11. Find them.
- Error redoA student adds 2x + y = 11 and x + y = 7 to get 3x + 2y = 18 and stops. What should be done?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 3, y = 2 | Subtracting removes x to give 2y = 4, so y = 2 and then 2x = 6. |
| 2 | x = 3, y = 4 | Subtracting gives 3y = 12 so y = 4, and then 3x = 9. |
| 3 | x = 4, y = 3 | Adding gives 10x = 40 so x = 4, and then 4y = 12. |
| 4 | x = 5, y = 2 | Subtracting removes y to leave x = 5, and then 2y = 4. |
| 5 | x = 5, y = 4 | Multiplying the first equation by 2 gives 2x + 2y = 18; subtracting leaves y = 4 and then x = 5. |
| 6 | x = 4, y = 5 | Multiplying the second equation by 2 gives 2x + 6y = 38; subtracting gives 5y = 25, so y = 5 and x = 4. |
| 7 | x = 4, y = 3 | The y coefficients are equal and opposite, so adding straight away gives 7x = 28. |
| 8 | x = 3, y = 4 | Both equations must be scaled: multiply the first by 2 and the second by 3 to get 6y and -6y, then add to obtain 19x = 57. |
| 9 | 28 and 17 | Call them x and y; adding x + y = 45 to x – y = 11 gives 2x = 56, so x = 28 and y = 17. |
| 10 | The y coefficients match, so subtract instead: x = 4, y = 3 | Adding only merges like terms and removes no unknown; subtracting removes y. |
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 →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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