How is this error-review paper different from the first three?

It targets the usual slips in elimination and substitution: solving only one equation, forgetting to substitute back, adding when you should subtract, and missing brackets.

How do I know the pair is correct?

Substitute both values into both original equations; only when both balance is the solution confirmed.

S2 Maths Simultaneous Equations Paper 4: Error Review

2026-11-09

Tutor Prep Guide · S2 Maths

Ten original error-review items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 revisit elimination by adding and subtracting, 4-6 cover substitution and brackets, 7-9 choose between adding and subtracting and apply the method to a word problem, and item 10 shows why a pair that fits only one equation must fail. Cover the answers first, then check each note.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S2 Maths Simultaneous Equations
Level	S2

02　Questions (10 items)

FoundationError review: solve x + y = 10 and x − y = 2.
FoundationError review: solve x + y = 7 and x − y = 1.
FoundationError review: given 2x = 8 and x + y = 9, find x and y.
IntermediateError review: solve 3x + 2y = 12 given that x = 2.
IntermediateError review: solve x + 2y = 8 with x = 2y.
IntermediateError review: solve 2x + y = 11 with y = x + 2.
ChallengeError review: solve 3x + 2y = 16 and 2x + 2y = 12.
ChallengeError review: solve 5x − 2y = 11 and 3x + 2y = 13.
ChallengeError review: 12 stamps made up of $2 and $5 stamps are worth $39 in total. How many of each?
Error redoError review: for x + y = 8 and x − y = 4 a pupil answers x = 4, y = 4. What is correct and what went wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	x = 6, y = 4	Adding gives 2x = 12 so x = 6, and substitution gives y = 4; x = 8 uses only one equation.
2	x = 4, y = 3	Adding gives 2x = 8 so x = 4, then y = 3 by substitution.
3	x = 4, y = 5	2x = 8 gives x = 4, then x + y = 9 gives y = 5.
4	y = 3	Substituting gives 6 + 2y = 12, so 2y = 6 and y = 3; missing the halving gives 6.
5	x = 4, y = 2	Substitute x = 2y to get 2y + 2y = 8, so y = 2 and x = 4.
6	x = 3, y = 5	Substituting gives 3x + 2 = 11, so x = 3 and y = 5.
7	x = 4, y = 2	Subtracting the equations removes y and gives x = 4; then 8 + 2y = 12 gives y = 2.
8	x = 3, y = 2	Adding removes y: 8x = 24 so x = 3; then 9 + 2y = 13 gives y = 2.
9	7 two-dollar and 5 five-dollar stamps	With x + y = 12 and 2x + 5y = 39, subtracting twice the first from the second gives 3y = 15, so y = 5 and x = 7.
10	x = 6, y = 2	Adding gives 2x = 12 so x = 6 and y = 2; 4 and 4 satisfy only the first equation, giving 0 instead of 4 in the second.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.