Module 2 · Algebra
Chapter 16: Linear Equations
Algebra
4 topics
🎯 1 practice questions
What this chapter covers
The 4 topics below make up Linear Equations on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
📚 Study this chapter
Notes, worked examples and hint-guided practice for every topic.
Start learning →
🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
Practice by topic →
📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
Take chapter test →
Formula Reference Sheet
This chapter
Single and standard forms
| Linear equation (one variable) | ax + b = 0 ⇒ x = −b/a (a ≠ 0) |
|---|---|
| Two-variable standard form | a₁x + b₁y = c₁ and a₂x + b₂y = c₂ |
| Slope–intercept line | y = mx + c (m = slope, c = y-intercept) |
| Cross-multiplication solution | x = (b₁c₂ − b₂c₁)/(a₁b₂ − a₂b₁) |
| Companion value | y = (c₁a₂ − c₂a₁)/(a₁b₂ − a₂b₁) |
Solution conditions for a pair
| Unique solution (lines meet) | a₁/a₂ ≠ b₁/b₂ |
|---|---|
| No solution (parallel lines) | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ |
| Infinite solutions (same line) | a₁/a₂ = b₁/b₂ = c₁/c₂ |
| Determinant test | D = a₁b₂ − a₂b₁; D ≠ 0 ⇒ unique |
| n equations need | n independent equations for n unknowns |
CAT reference
🖩 Graphing Calculator