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 (Intermediate, 10 Questions)

2026-11-08

Tutor Prep Guide · S2 Mathematics

The intermediate paper puts pairs of linear equations into context: clear fractions and decimals before solving, and set up the unknowns yourself for animal, age and shopping problems, with answers and notes.

Quick answer Answers in order: (5, 2), (3, 2), (4, 2), (6, 3), (6, 2), 27 and 9, 12 chickens and 8 rabbits, 17 and 12, pen 8 and notebook 5, (1, 2).

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 30 minutes
Difficulty mix	Intermediate 10
Chapter	Chapter: S2 Maths: Simultaneous Linear Equations
Level	S2

02 Questions (10 items)

IntermediateSolve 3x + 2y = 19 and x – y = 3.
IntermediateSolve 4x – 3y = 6 and 2x + y = 8.
IntermediateSolve 5x + 2y = 24 and 3x – 2y = 8.
IntermediateSolve x/2 + y/3 = 4 together with x + y = 9.
IntermediateSolve 0.5x + 0.2y = 3.4 with x + y = 8.
IntermediateTwo numbers add up to 36 and the larger is three times the smaller. Find them.
IntermediateA cage holds chickens and rabbits: 20 animals and 56 legs. How many of each?
IntermediateTwo brothers are 29 years old together and 5 years apart. Find their ages.
IntermediateThree pens and two notebooks cost 34 dollars in total, and each pen costs 3 dollars more than a notebook. Find the prices.
IntermediateSolve x + 2y = 5 and 2x – y = 0.

03 Answers and one-line notes

#	Answer	One-line note
1	x = 5, y = 2	From the second equation x = y + 3; substituting gives 3y + 9 + 2y = 19, so y = 2 and x = 5.
2	x = 3, y = 2	From the second equation y = 8 – 2x; substituting gives 4x – 24 + 6x = 6, so 10x = 30, x = 3 and y = 2.
3	x = 4, y = 2	Adding cancels the y terms and gives 8x = 32, so x = 4 and 20 + 2y = 24 gives y = 2.
4	x = 6, y = 3	Multiplying the first equation by 6 gives 3x + 2y = 24; combining it with x + y = 9 gives x = 6 and y = 3.
5	x = 6, y = 2	Multiplying by 10 gives 5x + 2y = 34; substituting y = 8 – x leaves 3x = 18, so x = 6 and y = 2.
6	27 and 9	With the smaller number y the larger is 3y, so 4y = 36, giving 9 and 27.
7	12 chickens and 8 rabbits	With c chickens and r rabbits, c + r = 20 and 2c + 4r = 56, which gives r = 8 and c = 12.
8	17 and 12	With x + y = 29 and x – y = 5, adding gives 2x = 34, so the elder is 17 and the younger 12.
9	pen 8, notebook 5	Let a notebook cost b, so a pen costs b + 3: 3(b + 3) + 2b = 34 gives b = 5 and the pen is 8.
10	x = 1, y = 2	The second equation gives y = 2x; substituting leaves x + 4x = 5, so x = 1 and y = 2.

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.