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S3 Maths: Simultaneous Linear Equations by Elimination (Paper 3 (challenge))
S3 Maths: Simultaneous Linear Equations by Elimination (Paper 3 (challenge))
Paper 3 (challenge): 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 3x + 2y = 16 and 5x – 2y = 16.
- FoundationSolve 4x + 3y = 22 and 7x – 3y = 22.
- FoundationSolve 2x + 3y = 7 and 4x – 3y = 23.
- IntermediateSolve 0.4x + 0.3y = 2.4 and 0.1x – 0.3y = -0.9.
- IntermediateAdult tickets cost x dollars and child tickets y dollars. Two adult and three child tickets cost 340; three adult and one child ticket cost 300. Find x and y.
- IntermediateSimplify first, then solve: 2(x + y) = x + 10 and 3(x – y) = y + 10.
- ChallengeSolve x + y = 12, y + z = 15 and x + z = 13.
- ChallengeTwo angles of a triangle are x and y degrees, with x + y = 110 and x – y = 30. Find both angles and the third angle.
- ChallengeTwo numbers add to 156 and one is twice the other. Find them.
- Error redoSolving 4x + 3y = 30 and 2x – 3y = 6, a student halves only the first equation and gets a wrong answer. What is the correct method?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 4, y = 2 | Adding removes y to give 8x = 32, so x = 4 and then 2y = 4. |
| 2 | x = 4, y = 2 | The y coefficients are opposite, so adding gives 11x = 44 and then 3y = 6. |
| 3 | x = 5, y = -1 | Adding gives 6x = 30 so x = 5, and then 3y = -3, which means y = -1. |
| 4 | x = 3, y = 4 | Adding removes y to give 0.5x = 1.5, so x = 3 and then 0.3y = 1.2. |
| 5 | x = 80, y = 60 | Scale the first equation by 3 and the second by 2, subtract to remove x, giving 7y = 420. |
| 6 | x = 6, y = 2 | Expanding gives x + 2y = 10 and 3x – 4y = 10; doubling the first and adding gives 5x = 30. |
| 7 | x = 5, y = 7, z = 8 | Adding all three gives 2(x + y + z) = 40, so the total is 20 and each unknown follows by subtraction. |
| 8 | x = 70, y = 40 and the third angle is 70 degrees | Adding gives 2x = 140 so x = 70; the angles of a triangle sum to 180, so the third is 180 minus 110. |
| 9 | 104 and 52 | Writing x + y = 156 and x – 2y = 0, subtracting gives 3y = 156. |
| 10 | Just add: 6x = 36, so x = 6 and y = 2 | The y coefficients are already equal and opposite, so adding directly removes y without scaling. |
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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