CBSE • Class 9 • Mathematics • Chapter 4 (Linear Equations in Two Variables) • Exercise 4.1

Exercise 4.1: Linear Equations in Two Variables — NCERT Solutions

Writing linear equations in standard form ax + by + c = 0.

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What this exercise covers

Standard formCoefficientsEquivalent equations

Step-by-step solutions — Exercise 4.1

3 solved questions • Each solution includes a Socratic hint, full working and a common-mistake callout • Last reviewed 2026-09-03

Exercise 4.1 Q1 • 2 marks

Express the equation 3x+7=5y3x + 7 = 5y in the standard form ax+by+c=0ax + by + c = 0 and state the values of aa, bb and cc.
Hint (Socratic — try this first)▾
Can you move every term to the left-hand side so that the right side becomes zero?
Step-by-step solution▾

Start with the given equation:

3x+7=5y3x + 7 = 5y

Bring all terms to the left-hand side:

3x−5y+7=03x - 5y + 7 = 0

Comparing with the standard form ax+by+c=0ax + by + c = 0:

  • a=3a = 3
  • b=−5b = -5
  • c=7c = 7
Common mistake:
Forgetting to change the sign of 5y5y when moving it across the equals sign, writing b=5b = 5 instead of b=−5b = -5.
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Exercise 4.1 Q2 • 2 marks

Write the equation y=−4xy = -4x in the form ax+by+c=0ax + by + c = 0 and identify aa, bb and cc.
Hint (Socratic — try this first)▾
What is the value of the constant term cc if there is no separate number on either side?
Step-by-step solution▾

Given:

y=−4xy = -4x

Move all terms to the left-hand side:

4x+y=04x + y = 0

Writing the constant term explicitly:

4x+y+0=04x + y + 0 = 0

Comparing with ax+by+c=0ax + by + c = 0:

  • a=4a = 4
  • b=1b = 1
  • c=0c = 0
Common mistake:
Writing b=0b = 0 because the yy has no visible coefficient, when in fact the coefficient of yy is 11.
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Exercise 4.1 Q3 • 2 marks

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Hint (Socratic — try this first)▾
If you let the cost of the notebook be one variable and the pen another, how do you write "twice"?
Step-by-step solution▾

Let the cost of a notebook be \rupee x\rupee\, x and the cost of a pen be \rupee y\rupee\, y.

The statement says the notebook costs twice the pen:

x=2yx = 2y

Writing in standard form:

x−2y=0x - 2y = 0

This is the required linear equation in two variables, with a=1a = 1, b=−2b = -2, c=0c = 0.

Common mistake:
Reversing the relationship and writing y=2xy = 2x (pen costs twice the notebook) instead of x=2yx = 2y.
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How to approach Exercise 4.1

  1. Re-read the chapter summary first. Open Linear Equations in Two Variables and refresh the key concepts: Linear equation, Standard form ax + by + c = 0, Ordered pair, Graph as a line.
  2. Try each problem yourself before opening the solution. Ten focused minutes per problem usually beats reading two finished solutions.
  3. Use Guru AI for the questions you get stuck on. The Socratic AI tutor walks you through it with hints instead of dictating the answer.
  4. Mark the questions you got wrong and revisit them after 24 hours — the spacing is what locks the method into long-term memory.

All exercises in Linear Equations in Two Variables

  1. Exercise 4.1 — Writing linear equations in standard form ax + by + c = 0.
  2. Exercise 4.2 — Solutions as ordered pairs — listing infinitely many solutions numerically.
  3. Exercise 4.3 — Graphing linear equations — drawing straight lines from intercepts.
  4. Exercise 4.4 — Lines parallel to axes — equations x = k and y = k and special cases.

Exercise 4.2 →

Solutions as ordered pairs — listing infinitely many solutions numerically.

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