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Linear Equations in Two Variables: CBSE Class 9 Maths knowledge organiser

Everything to know about 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

Linear equation in two variables
An equation that can be written ax + by + c = 0, with a and b not both zero.
Solution
An ordered pair (x, y) that makes the equation true.
Graph of the equation
A straight line: every point on it is a solution.

Key formulas

\(ax+by+c=0\) (\(a,b\) not both 0): infinitely many solutions, all on one straight line
\(x=a\) ∥ \(y\)-axis; \(y=b\) ∥ \(x\)-axis; intercepts: put \(y=0\), then \(x=0\)
A point is on the line exactly when its coordinates satisfy the equation; \(y=mx\) passes through the origin

Worked example

Is \((4, -1)\) a solution of \(x + 2y = 2\)?

\(4 + 2(-1) = 2\): yes.

Common mistakes

  • Substituting \(x\) and \(y\) the wrong way round when testing a point.
  • Saying the equation has one solution (or two): it has infinitely many.
  • Drawing \(x = 3\) as a horizontal line: it is vertical.
  • Forgetting the units or what \(x\) and \(y\) mean in a word problem.

You should be able to…

  • Write an equation in the form ax + by + c = 0, test a point and describe lines parallel to the axes.
  • Find solutions and intercepts, find an unknown coefficient and form an equation from a situation.
  • Build a linear model from a story, tabulate it and answer each part of a case study.
  • Find where lines meet the axes and each other, test collinearity and find areas cut off by lines.

The printable sheet

Linear Equations in Two Variables knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes
Linear Equations in Two Variables knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers