CBSE Mathematics 2026–27 · Topic 5

Linear Equations in Two Variables

Understand the idea, practise the reasoning and apply it in an investigation. These original notes follow the regular Class IX Mathematics syllabus; the Advanced course is separate.

What to learn

Be able to explain the key result, choose a method that fits the question, show reasoning clearly and verify the answer.

Core concepts

An equation ax+by+c=0 has ordered-pair solutions; each solution is a point on its straight-line graph. For y=mx+c, m is slope and c is the y-intercept.
Two equations model two constraints. Their graphs may intersect once, be parallel or coincide. Substitution and elimination find their common solution.
Interpret variables, units and the meaning of an intersection in context; check a solution in both original equations.

Original CBSE-style solved examples

Attempt each calculation before reading the solution.

Example · solve by elimination

Solve 2x+y=11 and x−y=1. Add: 3x=12, so x=4. Substitute: 4−y=1, hence y=3. Check: 8+3=11 and 4−3=1.

Example · slope and intercept

For y=2x+1, the slope is 2 and y-intercept is (0,1). The points (0,1), (1,3), (2,5) lie on the line because each pair satisfies the equation.

Practice questions with answers

1. Does (2,3) satisfy 3x+y=9?

Yes: 3×2+3=9.

2. Solve x+y=9 and x−y=3.

Add to get 2x=12, so x=6 and y=3.

Practical investigation

Compare two pretend taxi plans, each with a fixed fee and a per-kilometre rate. Write and graph both equations; interpret the intersection.

Keep a record of materials, steps, observations and conclusion.

Self-check

Can I state the definition or theorem precisely?
Can I explain why the method applies?
Did I check signs, units, labels and the final result?

Use your prescribed NCERT textbook and teacher’s sequence. These are original study notes, not copied textbook answers.