When should I substitute and when should I add or subtract the equations?

Substitution is fastest when one equation is already written as x = ... or y = ..., while adding or subtracting the two equations removes a variable at once when its coefficients match or are opposites.

Why check the answer in both equations?

Substituting into only one equation can satisfy that line but fail the other, so put the pair back into both equations and confirm both sides match.

S2 Maths: Simultaneous Linear Equations (Foundation, 10 Questions)

2026-11-08

Tutor Prep Guide · S2 Mathematics

A foundation set on the two entry methods for a pair of linear equations in two unknowns: add or subtract when the coefficients match, or substitute when one equation already gives y in terms of x. All ten answers are integers, each with a one-line note.

Quick answer Answers in order: (7, 3), (7, 5), (3, 5), (3, 6), (4, 2), (3, 4), (4, 1), (3, 2), (2, 3), and 13 with 7.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 25 minutes
Difficulty mix	Foundation 10
Chapter	Chapter: S2 Maths: Simultaneous Linear Equations
Level	S2

02 Questions (10 items)

FoundationSolve the simultaneous equations x + y = 10 and x – y = 4.
FoundationSolve x + y = 12 and x – y = 2.
FoundationSolve 2x + y = 11 with x = 3.
FoundationSolve y = 2x and x + y = 9.
FoundationSolve 3x + 2y = 16 with y = 2.
FoundationSolve 2x + y = 10 and x + 2y = 11.
FoundationSolve x – y = 3 and 2x + y = 9.
FoundationSolve 2x + 3y = 12 and 2x + y = 8.
FoundationSolve 5x + 2y = 16 and 3x + 2y = 12.
FoundationTwo numbers add up to 20 and differ by 6. Find them.

03 Answers and one-line notes

#	Answer	One-line note
1	x = 7, y = 3	Adding the two equations gives 2x = 14, so x = 7, and y = 3 follows from x + y = 10.
2	x = 7, y = 5	Adding gives 2x = 14 so x = 7, and subtracting gives 2y = 10 so y = 5.
3	x = 3, y = 5	Put x = 3 into the first equation: 6 + y = 11, so y = 5.
4	x = 3, y = 6	Substituting y = 2x gives x + 2x = 9, so x = 3 and y = 6.
5	x = 4, y = 2	Putting y = 2 gives 3x + 4 = 16, so 3x = 12 and x = 4.
6	x = 3, y = 4	Doubling the first equation gives 4x + 2y = 20; subtracting the second leaves 3x = 9, so x = 3 and y = 4.
7	x = 4, y = 1	Adding the equations gives 3x = 12, so x = 4 and y = 1 follows from x – y = 3.
8	x = 3, y = 2	Subtracting removes x and leaves 2y = 4, so y = 2 and then 2x + 2 = 8 gives x = 3.
9	x = 2, y = 3	Subtracting gives 2x = 4 so x = 2, and 10 + 2y = 16 then gives y = 3.
10	13 and 7	Let the numbers be x and y with x + y = 20 and x – y = 6; adding gives 2x = 26, so x = 13 and y = 7.

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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