Playbook
Linear Equations
40 q · 20% HARD · fading: 2.7 a paper in 2016-2020, one question in the six 2024-2026 papers. Learn it for word-problem fluency, which the arithmetic chapters use, not for its own weight.
- Questions in the bank
- 40
- q/paper (21 papers)
- 1.90
- Tagged HARD
- 20%
- Subtopics
- 4
Strand: Selective
When you’ll see it
Two unknowns and two conditions, an age problem, or a word problem to turn into equations.
How this chapter is tested
40 questions, but fading: 2.7 a paper in 2016-2020 and one question in the six 2024-2026 papers. It is still worth learning, because turning words into two equations is how most arithmetic questions are solved.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Solving a pair
Elimination or substitution; a pair with proportional coefficients has no unique solution.
Word problems
One equation per condition; name the unknowns first.
Age problems
Everyone ages by the same number of years.
Integral solutions
Count the whole-number solutions of ax + by = c by stepping through one variable.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Consistency
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ means no solution, not infinitely many.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Linear Equations notesDrill every Linear Equations question
40 questions from the bank, across 4 subtopics.
Drill one subtopic at a time
The 4 subtopics, in teaching order.
- Solving Linear SystemsDrill Solving Linear Systems
- Word Problems and ApplicationsDrill Word Problems and Applications
- Age ProblemsDrill Age Problems
- Integral Solutions and Diophantine EquationsDrill Integral Solutions and Diophantine Equations
Related playbooks
Often paired with this one — the technique or the trap overlaps. Drill these next.