This GCSE Maths simultaneous equations worksheet with answers is designed for focused GCSE revision. Simultaneous equations ask for values that satisfy two equations at the same time. Most GCSE questions can be handled by careful elimination.
Use it as a short practice task before moving into mixed exam questions. If you need more structured help, I also offer GCSE Maths tutoring and parent-friendly GCSE revision support.
Before you start
The level for this worksheet is Higher and confident Foundation. Work through the questions without checking the answers first. The point is not only to get the final answer, but to practise the method clearly enough that you could repeat it in a test.
Keep your working visible. GCSE Maths mark schemes often reward method, so a clear first line can still matter even if the arithmetic goes wrong later.
Skills this worksheet checks
This worksheet checks whether you can recognise common simultaneous equations question types, choose a sensible first step, and keep your working organised. Those three habits matter more than racing through the list.
For each question, write one line that explains the method before you calculate. That might be a formula, a common denominator, an equation, a route through a diagram, or the probability operation you are using. This makes the practice closer to the way marks are awarded in GCSE exams.
Worksheet questions
- Solve x + y = 9 and x - y = 3.
- Solve 2x + y = 11 and x + y = 7.
- Solve 3x + 2y = 16 and x + 2y = 8.
- Solve 2x + 3y = 18 and 2x + y = 10.
- Solve 4x + y = 19 and x + y = 7.
- Solve 2x + 5y = 29 and 3x + 5y = 34.
- Solve y = 2x + 1 and x + y = 10.
- Solve 3x - y = 8 and x + y = 12.
- Two apples and one banana cost £1.10. One apple and one banana cost 70p. Find each price.
- Solve 5x + 2y = 24 and 3x + 2y = 16.
Answers and method checks
| # | Question | Method | Answer |
|---|---|---|---|
| 1 | Solve x + y = 9 and x - y = 3. | Add the equations to get 2x = 12. | x = 6, y = 3 |
| 2 | Solve 2x + y = 11 and x + y = 7. | Subtract the second equation from the first. | x = 4, y = 3 |
| 3 | Solve 3x + 2y = 16 and x + 2y = 8. | Subtract to get 2x = 8. | x = 4, y = 2 |
| 4 | Solve 2x + 3y = 18 and 2x + y = 10. | Subtract to get 2y = 8. | x = 3, y = 4 |
| 5 | Solve 4x + y = 19 and x + y = 7. | Subtract to get 3x = 12. | x = 4, y = 3 |
| 6 | Solve 2x + 5y = 29 and 3x + 5y = 34. | Subtract to get x = 5, then substitute. | x = 5, y = 3.8 |
| 7 | Solve y = 2x + 1 and x + y = 10. | Substitute 2x + 1 for y. | x = 3, y = 7 |
| 8 | Solve 3x - y = 8 and x + y = 12. | Add the equations to eliminate y. | x = 5, y = 7 |
| 9 | Two apples and one banana cost £1.10. One apple and one banana cost 70p. Find each price. | Subtract the equations to find the apple price. | apple 40p, banana 30p |
| 10 | Solve 5x + 2y = 24 and 3x + 2y = 16. | Subtract to get 2x = 8. | x = 4, y = 2 |
How to mark this worksheet
Mark each question with more detail than a tick or cross. If the answer is wrong, label the error: method choice, arithmetic, notation, units, signs, calculator input, or not reading the question carefully.
For simultaneous equations, it is especially useful to redo the questions you missed after a short break. A topic can feel familiar immediately after reading the answer, but the real test is whether you can start the method independently later.
A good correction is specific. Instead of writing 'revise this', write the exact fix: choose a common denominator, show the multiplier, update the probability after the first choice, label the radius, or subtract the smaller coordinate from the larger one. Specific corrections make the next practice session much easier to plan.
Common mistakes
- Eliminating a variable before the coefficients match.
- Subtracting in the wrong order and losing signs.
- Finding one value but not substituting to find the other.
- Not checking both original equations.
Extension practice
After marking the worksheet, choose three questions and change one number in each. Keep the structure the same, then solve your new versions. This is a quick way to check whether you understand the method rather than remembering the original answer.
If the changed question becomes much harder, that is useful information. It usually means the method is not fully secure yet, or that a small change has introduced a new skill such as negative numbers, fractions, unit conversion, exact form, or a second step.
Students aiming for higher grades should also write one short explanation question. For example: explain why this vector is parallel, explain why these two routes must be added, explain why this theorem applies, or explain why the original amount is not the same as the sale amount. These explanations build the reasoning marks that many students miss.
What to practise next
Once you can complete this worksheet accurately, move to mixed questions where the topic is not written in the title. That is closer to the exam, because you have to recognise the method as well as carry it out.
You can also use the Maths practice papers hub to connect topic practice with broader exam-style work. If the same mistake keeps appearing, bring that exact question to a lesson or send it to me so we can work out what is blocking the method.
