How to solve simultaneous equations
Use this guide to review the main routes for simultaneous equations before trying your own system in CureMath — AI Math Explainer.
Start here if you want the short version before reading the full method.
- Solve simultaneous equations by finding values that make both equations true at the same time.
- Elimination is often fastest when coefficients line up cleanly, while substitution is often 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 make both equations true at the same time.
This page works best as the practical overview before you branch into a method-specific page.
One reliable route through the topic.
- 1Write both equations in aligned form.
- 2Choose whether elimination or substitution gives the cleaner route.
- 3If using elimination, match the coefficients and remove one variable by adding or subtracting.
- 4If using substitution, isolate one variable first and place it into the other equation.
- 5Solve the remaining equation and substitute back for the second variable.
- 6Check both values in both original equations.
Choose the route that fits the quadratic.
Use it when the same variable can be removed by adding or subtracting the equations.
Use it when one equation already gives you x or y directly, or can be rearranged quickly.
See the method in action.
x + y = 11 and x - y = 1
- Add the equations to get 2x = 12.
- So x = 6.
- Substitute back to get y = 5.
y = 2x + 1 and x + y = 10
- Substitute y = 2x + 1 into x + y = 10.
- This gives 3x + 1 = 10, so x = 3.
- Substitute back to get y = 7.
Things that commonly send the method off track.
- Choosing elimination when substitution would have made the arithmetic much shorter.
- Eliminating the wrong term because the equations were not aligned clearly.
- Solving one variable correctly but forgetting to substitute back for the second.
Use a short verification pass before moving on.
- Check the final values in both original equations, not only in the simplified line you used while solving.
- If one method feels awkward halfway through, pause and see whether the other method would shorten the route.
Try a few variations before switching to a calculator or solver tool.
- x + y = 14 and x - y = 4
- 2x + y = 13 and x - y = 1
- y = 3x - 2 and x + y = 10
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Extra algebra revision resources
If you want more printed algebra practice after this page, these broader searches are a sensible next step.
Amazon
Algebra workbook and revision book search
Useful if you want more equation, factorising, and worked-example practice in one printed source.
View Algebra workbook and revision book searchAmazon
GCSE algebra practice resources search
A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
View GCSE algebra practice resources searchNeed live help with simultaneous equations?
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Short answers worth checking.
Substitution is often quicker when one equation already isolates a variable easily.
Put both values into both original equations and confirm that both statements 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.