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S3 Maths: Simultaneous Linear Equations by Elimination (Paper 4 (error clinic))
S3 Maths: Simultaneous Linear Equations by Elimination (Paper 4 (error clinic))
Paper 4 (error clinic): 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 = 9 and x – y = 5.
- FoundationSolve 2x + y = 10 with y = 4.
- FoundationSolve 3x – y = 7 with y = 2.
- IntermediateSolve 5x + 2y = 24 and 3x – 2y = 8.
- IntermediateSolve 2x + 3y = 13 and 4x – 3y = 17.
- IntermediateSolve x + 2y = 10 and x – 2y = -2.
- ChallengeSolve 3x + 5y = 29 and 2x – 5y = -14.
- ChallengeSolve 4x + 7y = 40 and 6x – 7y = -10.
- ChallengeThere are 20 coins in total, made of a five-dollar coins and b two-dollar coins, worth 70 dollars. Find a and b.
- Error redoSolving x + 3y = 11 and 2x – 3y = 4, a student adds and writes x = 15 without dividing by the coefficient. What is the correct answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 7, y = 2 | Adding gives 2x = 14 so x = 7, and substituting back gives y = 2. |
| 2 | x = 3, y = 4 | Substituting y = 4 gives 2x = 6, so x = 3. |
| 3 | x = 3, y = 2 | Substituting y = 2 gives 3x = 9, so x = 3. |
| 4 | x = 4, y = 2 | Adding removes y to give 8x = 32, so x = 4 and then 2y = 4. |
| 5 | x = 5, y = 1 | Adding gives 6x = 30 so x = 5, and then 3y = 3. |
| 6 | x = 4, y = 3 | Adding gives 2x = 8 so x = 4, and then 2y = 6. |
| 7 | x = 3, y = 4 | The y terms are opposite, so adding gives 5x = 15 and then 5y = 20. |
| 8 | x = 3, y = 4 | Adding gives 10x = 30 so x = 3, and then 7y = 28. |
| 9 | a = 10, b = 10 | From a + b = 20 and 5a + 2b = 70, doubling the first and subtracting gives 3a = 30. |
| 10 | x = 5, y = 2 | Adding gives 3x = 15, which must still be divided by 3 to get x = 5, and then 3y = 6. |
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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