GCSE simultaneous equations guide
Use this guide for a quick revision-style walkthrough, then test your own pair of equations in the app.
Start here if you want the short version before reading the full method.
- GCSE simultaneous-equations questions usually ask you to find the values that make two equations true at the same time.
- At this level, elimination is often the fastest route, but substitution can be cleaner when one variable is already isolated.
What this topic means and what to look for first.
Simultaneous equations are solved by finding values that satisfy both equations at the same time.
At GCSE level, elimination is often the fastest route.
One reliable route through the topic.
- 1Write both equations in a tidy aligned form.
- 2Choose a variable to eliminate.
- 3Multiply one or both equations if needed so the coefficients match.
- 4Add or subtract the equations to remove one variable.
- 5Solve for the remaining variable and substitute back.
See the method in action.
x + y = 10 and x - y = 2
- Add the equations to get 2x = 12.
- So x = 6.
- Substitute into x + y = 10 to get y = 4.
2x + y = 9 and x - y = 0
- Add the equations to eliminate y.
- This gives 3x = 9, so x = 3.
- Substitute back to get y = 3.
Things that commonly send the method off track.
- Adding when you meant to subtract, or vice versa.
- Forgetting to substitute the solved value back into one original equation.
Use a short verification pass before moving on.
- Put both values back into both original equations, not just one of them.
- Check whether the arithmetic still works after any multiplied or subtracted equation step.
Try a few variations before switching to a calculator or solver tool.
- x + y = 13 and x - y = 1
- 2x + y = 11 and x - y = 1
- 3x + 2y = 16 and x + 2y = 8
Want to try a similar problem yourself?
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Revision resources for simultaneous equations
If you want more printed practice after this guide, these GCSE-style resources are a sensible next step.
Amazon
GCSE maths revision books for simultaneous equations
A broader GCSE revision search if you want worked examples and mixed algebra practice in one place.
View GCSE maths revision books for simultaneous equationsAmazon
Simultaneous equations practice workbook search
Useful if you want a workbook-style route with more repetition than a single online guide page.
View Simultaneous equations practice workbook searchNeed live help with simultaneous equations?
If this revision page still leaves the topic stuck, use the live-help route to describe the exact equation style or exam level you need help with.
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Short answers worth checking.
Often yes at GCSE, especially when coefficients line up easily.
Substitute both values into both original equations and confirm both are true.
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.