How to check simultaneous equation answers
Use this page when you already have values for x and y and want to verify them properly before relying on the result.
Start here if you want the short version before reading the full method.
- The fastest reliable check is to substitute the final values into both original equations.
- If both equations stay true with the same pair of values, the simultaneous-equation answer is correct.
What this topic means and what to look for first.
A simultaneous-equation answer is only valid if the same pair of values works in both equations at once.
That is why checking only one line is not enough, even if the arithmetic there looks fine.
One reliable route through the topic.
- 1Write the original two equations again so you do not accidentally check against a rearranged working line.
- 2Substitute the final x and y values into the first equation and simplify.
- 3Substitute the same x and y values into the second equation and simplify.
- 4If both statements are true, the answer is correct. If one fails, retrace the step where the variables were separated or eliminated.
See the method in action.
Check x = 6 and y = 4 for x + y = 10 and x - y = 2
- In the first equation, 6 + 4 = 10, so it works.
- In the second equation, 6 - 4 = 2, so it also works.
- Because the same pair satisfies both equations, the answer is correct.
Check x = 3 and y = 2 for 2x + y = 11 and x - y = 1
- In the first equation, 2(3) + 2 = 8, not 11.
- That already shows the pair is wrong, even though the second equation gives 3 - 2 = 1.
- A simultaneous-equation answer must satisfy both equations, not just one.
Things that commonly send the method off track.
- Checking the values in only one equation and assuming the system is solved.
- Substituting into a rearranged working line instead of the original equations.
- Using the wrong sign when substituting a negative value.
Use a short verification pass before moving on.
- Check the same pair of values in both original equations.
- Use brackets around negative substitutions so the signs stay correct.
- If one equation works and the other does not, go back to the elimination or substitution step rather than only rechecking the final line.
Try a few variations before switching to a calculator or solver tool.
- Check x = 4 and y = 3 for 2x + y = 11 and x - y = 1
- Check x = 5 and y = 2 for x + y = 7 and 2x - y = 8
- Check x = 2 and y = 5 for y = x + 3 and x + y = 7
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Short answers worth checking.
Substitute the final values into both original equations and confirm that both statements are true.
A simultaneous-equations solution must satisfy both equations at the same time, not just one of them.
Check against the original equations because intermediate working lines may already contain a slip.
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.
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