y=k x=k ax+by+c=0 ∞ solutions verify: sub (a,b)
ax+by=c
Chapter 4  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Linear Equations in Two Variables

One Line, Infinite Solutions — Understand the Graph Behind the Equation

📋 45 MCQs ⭐ 24 PYQs ⏱ 60 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

45Total MCQs
20Easy
18Medium
7Hard
24PYQs
60 secAvg Time/Q
6Topics
Easy 44% Medium 40% Hard 16%

Why Practise These MCQs?

CBSE Class IXNTSEState Boards

Linear Equations in Two Variables at Class IX level focuses on the concept of a solution, infinitely many solutions, graphical representation as a straight line, and equations of axes-parallel lines. CBSE MCQs test whether a given point satisfies an equation and what the graph looks like. NTSE includes elegant word-problem-to-equation conversion. This chapter bridges arithmetic and coordinate geometry.

Topic-wise MCQ Breakdown

Standard Form ax + by + c = 05 Q
Solutions of a Linear Equation10 Q
Graph: Straight Line Through Origin8 Q
Graph: Lines Parallel to Axes8 Q
Equations of x-axis and y-axis6 Q
Word Problems → Linear Equation8 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$ax + by + c = 0\ (a,b\ \text{not both zero})$
$\text{y = 0: equation of x-axis}$
$\text{x = 0: equation of y-axis}$
$\text{x = k: line parallel to y-axis}$
$\text{y = k: line parallel to x-axis}$
$\text{Infinitely many solutions exist for one equation in two variables}$

MCQ Solving Strategy

To check if a point (a, b) satisfies an equation, substitute x = a, y = b and verify the equality. For graph-type MCQs: every linear equation in x and y graphs as a straight line; y = constant is horizontal; x = constant is vertical. If the equation has only x (like 2x = 6), the graph is a vertical line. If only y, the graph is horizontal. Word problem MCQs: define the two variables, write one equation in two unknowns.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Verify if a point is a solution, identify standard form, write simple equations

② Medium

Graph identification (horizontal/vertical/through origin), find missing coordinate

③ Hard

Word problem to equation conversion, geometric interpretation of lines

★ PYQ

CBSE — solution verification + graph type; NTSE — equation modelling

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Introduction to Euclid's Geometry
🎯 Knowledge Check

Maths — LINEAR EQUATIONS IN TWO VARIABLES

50 Questions Class 9 MCQs
1
A linear equation in two variables represents a
2
The general form of a linear equation in two variables is
3
In the equation \(2x + 3y = 6\), the coefficient of \(y\) is
4
Which of the following is a linear equation in two variables?
5
The equation \(y = 0\) represents
6
The equation \(x = 0\) represents
7
How many solutions can a linear equation in two variables have?
8
The coordinates (0, 3) satisfy which of the following equations?
9
If \(x = 2\), \(y = 3\) satisfy \(2x + 3y = k\), then\( k =\)
10
Which of the following points lies on the line \(x + y = 4\)?
11
The graph of \(x = 5\) is
12
The graph of \(y = 2\) is
13
In \(ax + by + c = 0\), if \(a = 0\), the equation becomes
14
In \(ax + by + c = 0\), if \(b = 0\), the equation represents
15
The pair \((x, y)\) satisfying \(y = 3x\) is
16
The graph of \(y = x\) passes through
17
If (2, 3) is a solution of \(3x + ky = 12\), find \(k\).
18
The \(x\)-intercept of \(2x + 3y = 6\) is
19
The \(y\)-intercept of \(2x + 3y = 6\) is
20
The equation of \(x\)-axis is
21
The equation of \(y\)-axis is
22
The point (–1, 0) lies on
23
The point (0, 4) lies on
24
The slope of line \(y = x\) is
25
If \(x = 2\) and \(y = 3\) satisfy \(ax + by = 12\), then \(2a + 3b\) =
26
Which of the following equations represents a line parallel to \(y\)-axis?
27
Which of the following equations represents a line parallel to \(x\)-axis?
28
If the graph of an equation passes through (0, 0), the equation is
29
In equation \(2x + 3y = 12\), if \(y = 0\), then \(x =\)
30
Which of the following is NOT a linear equation in two variables?
31
The equation \(y = 2x + 1\) cuts the \(y\)-axis at
32
The point where the line crosses the \(x\)-axis has
33
The line \(3x + 2y = 12\) meets\( x\)-axis at
34
The line \(3x + 2y = 12\) meets \(y\)-axis at
35
In the equation \(ax + by + c = 0\), the constants \(a\) and \(b\) cannot be
36
Equation of a line passing through (0, 2) and parallel to \(x\)-axis is
37
Equation of line passing through (3, 0) and parallel to\( y\)-axis is
38
The equation \(0x + y = 4\) represents
39
The equation \(x + 0y = 5\) represents
40
Which of the following points does NOT lie on \(y = 2x\)?
41
Which of these represents a family of lines passing through origin?
42
If \(x = 2\), \(y = 1\) satisfy \(3x – 2y = k\), then \( k =\)
43
Which of the following is the equation of \(x\)-axis?
44
The equation of the line passing through (0, 0) and (2, 2) is
45
The equation \(4x + 2y = 8\) is equivalent to
46
The point (0, 0) satisfies the equation
47
The equation \(3x – 5y + 7 = 0\) has slope
48
The line \(y = –x\) passes through
49
The graph of \(x + y = 0\) passes through
50
The line \(y = 3x + 2\) cuts the \( y\)-axis at
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Class 9 Linear Equations MCQs with Answers
Class 9 Linear Equations MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
Mastering linear equations in two variables is essential for Class 9 Mathematics. This chapter introduces the concept of equations involving two variables, their solutions, and graphical representation. To help students practice and revise effectively, we have prepared 50 multiple-choice questions (MCQs) covering all key topics, including the general form of linear equations, finding solutions, x- and y-intercepts, slopes, and plotting lines on a graph. These MCQs are ideal for quick practice,…
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    LINEAR EQUATIONS IN TWO VARIABLES — Learning Resources

    📄 Detailed Notes
    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Exercise-4.1 Exercise-4.2
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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Class 9 Linear Equations MCQs with Answers
    Class 9 Linear Equations MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
    Mastering linear equations in two variables is essential for Class 9 Mathematics. This chapter introduces the concept of equations involving two variables, their solutions, and graphical representation. To help students practice and revise effectively, we have prepared 50 multiple-choice questions (MCQs) covering all key topics, including the general form of linear equations, finding solutions, x- and y-intercepts, slopes, and plotting lines on a graph. These MCQs are ideal for quick practice,…
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
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    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/linear-equations-in-two-variables/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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