Match coefficients
Scale one or both equations so one variable has coefficients of equal size.
AQA 8300 · A19 · Simultaneous equations
Simultaneous equations: add or subtract to eliminate
The elimination mark. If the matched coefficients do not cancel, the variable is still present and every line after it is working on the wrong equation.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Eliminate
Add when the matched coefficients have opposite signs, subtract when they share a sign.
Substitute and pair
Solve for the remaining variable, substitute back, and give the solution as an ordered pair.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Adding the equations when the matched coefficients share a sign, or subtracting when they differ, so the variable does not actually eliminate.
02
Why it survives revision
A sign slip still produces a solvable equation and a pair of numbers that look like an answer. Substituting back into the same equation used to derive them can even appear to confirm it — the check has to use the OTHER equation to catch this, and it usually does not.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Look at the sign of the matched coefficients first, then choose add or subtract. Verify in the equation you did not use.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form needs both equations scaled before anything matches, so the choice has to be made after the multiplication rather than before.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: A19 · Simultaneous equations. Elimination, recovery and ordered-pair accuracy. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
Do I add or subtract the two equations?
Look at the signs of the matched coefficients. Same sign: subtract. Opposite signs: add. Getting it backwards still produces a pair of numbers, which is why it is easy to miss.
How do I check my answer?
Substitute into the equation you did NOT use to find the second variable. Checking in the equation you just used can confirm a wrong answer.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence