Knowledge organisers

Pair of Linear Equations in Two Variables: CBSE Class 10 Maths knowledge organiser

Everything to know about pair of linear equations in two variables on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Pair of linear equations: Two linear equations in the same two variables, each a straight line.
Consistent: The pair has at least one solution: the lines meet or coincide.
Inconsistent: The pair has no solution: the lines are parallel.

Key formulas

\(a_1x+b_1y+c_1=0\), \(a_2x+b_2y+c_2=0\)
Unique solution (lines intersect)	\(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\)
No solution (parallel, inconsistent)	\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\)
Infinitely many (coincident)	\(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Solve by substitution or elimination; consistent = at least one solution

Worked example

Solve \(4x + 3y = 18,\ 2x - y = 4\). From the second, \(y = 2x - 4\); then \(4x + 6x - 12 = 18 \Rightarrow x = 3,\ y = 2\).

Common mistakes

Comparing only \(a\) and \(b\) ratios and forgetting \(c\) when deciding between parallel and coincident.
Sign errors when subtracting equations; check the answer in both original equations.
“Consistent” means at least one solution — not necessarily a unique one.
In graphs: unlabelled axes/lines, or too few points plotted.

You should be able to…

Solve a pair of equations by substitution or elimination and tell from the ratios whether lines meet, are parallel or coincide.
Find k for a given number of solutions, solve by the graph, and turn a board-style word problem into two equations.
Produce neat graphs with labelled lines and complete word-problem solutions that define variables and state the final answer.
Handle consistency questions with two unknowns, clever combinations of the solution and the slightly unusual word problems that separate 95+ scripts.

The printable sheet

Pair of Linear Equations in Two Variables knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Pair of Linear Equations in Two Variables knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers