GCSE simultaneous equations revision questions
Use this page when you want short GCSE-style simultaneous-equations practice rather than a long concept lesson.
Start here if you want the short version before reading the full method.
- Most GCSE simultaneous-equations questions can be solved by elimination, but some are quicker by substitution.
- The most important final habit is to check both values in both original equations.
What this topic means and what to look for first.
This page is designed for revision pace: short examples, a small spread of question types, and a clear self-check routine.
It works best when paired with the method pages, so you can jump out to elimination or substitution only when needed.
One reliable route through the topic.
- 1Start by deciding whether elimination or substitution is shorter for the question in front of you.
- 2Solve one variable first and then substitute back for the second.
- 3Check the final pair in both original equations before moving on to the next practice question.
See the method in action.
x + y = 10 and x - y = 2
- Add the equations to get 2x = 12, so x = 6.
- Substitute back into x + y = 10 to get y = 4.
y = x + 1 and x + y = 9
- Substitute y = x + 1 into x + y = 9.
- This gives 2x + 1 = 9, so x = 4 and y = 5.
Things that commonly send the method off track.
- Forgetting to multiply every term when scaling an equation in elimination.
- Losing a sign after substitution because brackets were skipped.
- Checking the answer in only one equation because the first check happened to work.
Use a short verification pass before moving on.
- Check both final values in both original equations.
- If a question felt awkward, ask whether the other method would have shortened the route.
Try a few variations before switching to a calculator or solver tool.
- x + y = 12 and x - y = 4
- 2x + y = 11 and x - y = 1
- 3x + 2y = 18 and x + 2y = 10
- y = 2x + 3 and x + y = 12
- y = 3x - 1 and 2x + y = 14
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Short answers worth checking.
Elimination is very common, but substitution also appears and can be the cleaner route when a variable is already isolated.
Put both values into both original equations and make sure both statements remain true.
Pause and check whether a different method would simplify the route before pushing through avoidable algebra clutter.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.