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Linear Equations in Two Variables Notes: Class 9 Maths Chapter 4

Class 9 Maths Chapter 4 Linear Equations in Two Variables covers the general form ax + by + c = 0, solutions of a linear equation, graphing linear equations, and equations of lines parallel to the axes.

Overview of Topics & Subtopics (Click to Jump)

1. Linear Equation in Two Variables

Short Note:

• An equation of the form ax + by + c = 0, where a, b, c are real numbers and a, b are not both zero, is called a linear equation in two variables.

• A pair of values of x and y satisfying the equation is called a solution. A linear equation in two variables has infinitely many solutions.

2. Graph of a Linear Equation

Short Note:

• Every solution (x, y) of a linear equation in two variables corresponds to a point on the line representing the equation, and the graph is always a straight line.

• To draw the graph, find at least two solutions, plot them, and join them with a line extended in both directions.

3. Equations of Lines Parallel to the Axes

Short Note:

• The equation x = a represents a line parallel to the y-axis, at a distance 'a' from it.

• The equation y = b represents a line parallel to the x-axis, at a distance 'b' from it.

NCERT Textbook Exercise Questions

Write four solutions for the equation 2x + y = 7.
Answer: Choosing values of x: x = 0 ⇒ y = 7 → (0, 7); x = 1 ⇒ y = 5 → (1, 5); x = 2 ⇒ y = 3 → (2, 3); x = 3 ⇒ y = 1 → (3, 1).
Check whether (2, 0) is a solution of x − 2y = 4.
Answer: Substitute x = 2, y = 0: 2 − 2(0) = 2 ≠ 4. So (2, 0) is not a solution.
Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
Answer: Any line of the form y = 7x, or x + y = 16, etc. passes through (2, 14) if it satisfies the point. There are infinitely many such lines because infinitely many lines can pass through a single point.
Draw the graph of the equation y = 3x.
Answer: Find solutions: x = 0 ⇒ y = 0; x = 1 ⇒ y = 3; x = −1 ⇒ y = −3. Plot (0,0), (1,3), (−1,−3) and join them to get a straight line through the origin.
If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
Answer: Substitute x = 3, y = 4: 3(4) = a(3) + 7 ⇒ 12 = 3a + 7 ⇒ 3a = 5 ⇒ a = 5/3.
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Class 9 › Mathematics › Linear Equations in Two Variables
Chapter notesRead the chapterPractice MCQsCheck what you rememberChapter test10 questions on one pageOnline testTest 1, 2 and 3, one question at a timePYQPrevious year questionsStudy materialPDF notes
Topics in this chapter: Linear Equation in Two VariablesGraph of a Linear EquationEquations of Lines Parallel to the Axes