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

⚠A linear equation in two variables has INFINITE solutions, not just one
⚠x = 3 graphs as a VERTICAL line, not a point on the x-axis
⚠y = 0 is the x-axis (all points have y = 0 there)
⚠x = 0 is the y-axis (all points have x = 0 there)
⚠Verify solutions by substituting BOTH coordinates — not just one

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

A linear equation in two variables represents a

a a. Point b b. Line c c. Parabola d d. Circle

The general form of a linear equation in two variables is

a a. $ax + b = 0$ b b. $ax² + by = c$ c c. $ax + by + c = 0$ d d. $ax² + by² + c = 0$

In the equation $2x + 3y = 6$, the coefficient of $y$ is

a a. 2 b b. 3 c c. 6 d d. 1

Which of the following is a linear equation in two variables?

a a. $x + y = 2$ b b. $x² + y = 2$ c c. $xy = 2$ d d. $y² = 3x$

The equation $y = 0$ represents

a a. X-axis b b. Y-axis c c. Origin d d. A line parallel to X-axis

The equation $x = 0$ represents

a a. X-axis b b. Y-axis c c. Line parallel to Y-axis d d. Diagonal line

How many solutions can a linear equation in two variables have?

a a. One b b. Two c c. Infinite d d. None

The coordinates (0, 3) satisfy which of the following equations?

a a. $x + y = 3$ b b. $2x + y = 3$ c c. $y = 3x$ d d. $x – y = 3$

If $x = 2$, $y = 3$ satisfy $2x + 3y = k$, then$ k =$

a a. 6 b b. 10 c c. 13 d d. 12

Which of the following points lies on the line $x + y = 4$?

a a. (0, 4) b b. (1, 1) c c. (3, 1) d d. (2, 3)

The graph of $x = 5$ is

a a. A horizontal line b b. A vertical line c c. A slant line d d. A parabola

The graph of $y = 2$ is

a a. A vertical line b b. A horizontal line c c. A diagonal line d d. A parabola

In $ax + by + c = 0$, if $a = 0$, the equation becomes

a a. Parallel to X-axis b b. Parallel to Y-axis c c. Origin d d. A curve

In $ax + by + c = 0$, if $b = 0$, the equation represents

a a. Line parallel to X-axis b b. Line parallel to Y-axis c c. Y-axis itself d d. A parabola

The pair $(x, y)$ satisfying $y = 3x$ is

a a. (1, 3) b b. (2, 1) c c. (3, 9) d d. (1, 1)

The graph of $y = x$ passes through

a a. (0, 0) b b. (1, 0) c c. (0, 1) d d. (2, 1)

If (2, 3) is a solution of $3x + ky = 12$, find $k$.

a a. 2 b b. 3 c c. 4 d d. 5

The $x$-intercept of $2x + 3y = 6$ is

a a. 2 b b. 3 c c. 6 d d. 4

The $y$-intercept of $2x + 3y = 6$ is

a a. 2 b b. 3 c c. 6 d d. 4

The equation of $x$-axis is

a a. $y = 0$ b b. $x = 0$ c c. $x + y = 0$ d d. $y = 1$

The equation of $y$-axis is

a a. $x = 0$ b b. $y = 0$ c c. $x = y$ d d. $x + y = 0$

The point (–1, 0) lies on

a a. X-axis b b. Y-axis c c. Origin d d. None

The point (0, 4) lies on

a a. X-axis b b. Y-axis c c. Origin d d. Line $y = x$

The slope of line $y = x$ is

a a. 0 b b. 1 c c. –1 d d. 2

If $x = 2$ and $y = 3$ satisfy $ax + by = 12$, then $2a + 3b$ =

a a. 12 b b. 6 c c. 9 d d. 15

Which of the following equations represents a line parallel to $y$-axis?

a a. $x = 3$ b b. $y = 3$ c c. $y = 0$ d d. $x + y = 0$

Which of the following equations represents a line parallel to $x$-axis?

a a. $y = 5$ b b. $x = 5$ c c. $x + y = 5$ d d. $x – y = 5$

If the graph of an equation passes through (0, 0), the equation is

a a. $y = mx$ b b. $y = mx + c$ c c. $x + y = 1$ d d. $y = x + 1$

In equation $2x + 3y = 12$, if $y = 0$, then $x =$

a a. 6 b b. 4 c c. 2 d d. 3

Which of the following is NOT a linear equation in two variables?

a a. $2x + 3y = 6$ b b. $x² + y = 1$ c c. $ x + y = 2$ d d. $x – 2y + 3 = 0$

The equation $y = 2x + 1$ cuts the $y$-axis at

a a. (0, 1) b b. (1, 0) c c. (0, 2) d d. (1, 2)

The point where the line crosses the $x$-axis has

a a. $y = 0$ b b. $x = 0$ c c. $x = y$ d d. $x = 1$

The line $3x + 2y = 12$ meets$ x$-axis at

a a. (4, 0) b b. (0, 6) c c. (3, 0) d d. (0, 4)

The line $3x + 2y = 12$ meets $y$-axis at

a a. (0, 6) b b. (6, 0) c c. (4, 0) d d. (0, 4)

In the equation $ax + by + c = 0$, the constants $a$ and $b$ cannot be

a a. Both zero b b. Both equal c c. Both negative d d. Integers

Equation of a line passing through (0, 2) and parallel to $x$-axis is

a a. $y = 2$ b b. $x = 2$ c c. $y = 0$ d d. $x + y = 2$

Equation of line passing through (3, 0) and parallel to$ y$-axis is

a a. $x = 3$ b b. $y = 3$ c c. $x + y = 3$ d d. $y = 0$

The equation $0x + y = 4$ represents

a a. $y = 4$ b b. $x = 4$ c c. $x = y$ d d. $x + y = 4$

The equation $x + 0y = 5$ represents

a a. $x = 5$ b b. $y = 5$ c c. $y = 0$ d d. $x + y = 5$

Which of the following points does NOT lie on $y = 2x$?

a a. (0, 0) b b. (1, 2) c c. (2, 3) d d. (3, 6)

Which of these represents a family of lines passing through origin?

a a. $y = mx$ b b. $y = mx + c$ c c. $x + y = c$ d d. $y = c$

If $x = 2$, $y = 1$ satisfy $3x – 2y = k$, then $ k =$

a a. 4 b b. 6 c c. 3 d d. 2

Which of the following is the equation of $x$-axis?

a a. $y = 0$ b b. $x = 0$ c c. $y = 1$ d d. $x + y = 0$

The equation of the line passing through (0, 0) and (2, 2) is

a a. $y = x$ b b. $y = 2x$ c c. $y = x + 2$ d d. $y = x – 2$

The equation $4x + 2y = 8$ is equivalent to

a a. $2x + y = 4$ b b. $x + y = 4$ c c. $x + y = 2$ d d. $2x + y = 8$

The point (0, 0) satisfies the equation

a a. $x + y = 0$ b b. $x – y = 0$ c c. $y = 2x$ d d. All of these

The equation $3x – 5y + 7 = 0$ has slope

a a. 3/5 b b. –3/5 c c. 5/3 d d. –5/3

The line $y = –x$ passes through

a a. (1, –1) b b. (1, 1) c c. (2, 2) d d. (0, 1)

The graph of $x + y = 0$ passes through

a a. (1, –1) b b. (1, 1) c c. (0, 1) d d. (1, 0)

The line $y = 3x + 2$ cuts the $ y$-axis at

a a. (0, 2) b b. (2, 0) c c. (0, 3) d d. (3, 0)

📚

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

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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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Frequently Asked Questions

A linear equation in two variables is an equation that can be written in the form ax+by+c=0, where a and b are real numbers, and a and b are not both zero.

Key topics include forming linear equations, representing them graphically, finding solutions, and understanding methods like substitution, elimination, and cross multiplication.

The standard form is ax + by + c = 0.

The coefficients ‘a’ and ‘b’ determine the slope and orientation of the straight line on the Cartesian plane.

It has infinitely many solutions, each corresponding to a point on its straight-line graph.

It is represented by a straight line on the Cartesian plane, showing all possible (x, y) solutions.

Examples include x+y=5, 2x-3y=7, and 4x+y=9.

Only if the constant term c=0; otherwise, (0, 0) may not satisfy the equation.

A one-variable equation has a single solution represented by a point on the number line, while a two-variable equation has infinite solutions represented by a line.

It refers to all pairs (x,y) that satisfy the equation and make both sides equal.

By choosing different values of x, calculating corresponding y values, plotting those points, and joining them to form a straight line.

It is y=mx+c, where m is the slope of the line andcccis the y-intercept.

It shifts the line horizontally or vertically depending on its value.

They are solved by methods like substitution, elimination, graphical interpretation, or cross multiplication.

Because real-life problems often require solving two related conditions simultaneously, such as profit and cost or speed and time.

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

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Linear Equations in Two Variables

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR EQUATIONS IN TWO VARIABLES

Frequently Asked Questions

Recent Posts

LINEAR EQUATIONS IN TWO VARIABLES — Learning Resources

Let's Connect

Linear Equations in Two Variables

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — LINEAR EQUATIONS IN TWO VARIABLES

Frequently Asked Questions

Q 01 What is a linear equation in two variables?

Q 02 What are the key topics covered in NCERT Class 9 Maths Chapter 4?

Q 03 What is the standard form of a linear equation in two variables?

Q 04 What do the coefficients ‘a’ and ‘b’ represent in a linear equation?

Q 05 How many solutions does a linear equation in two variables have?

Q 06 What is the graphical representation of a linear equation in two variables?

Q 07 What are the examples of linear equations in two variables?

Q 08 Can a linear equation have both x and y equal to zero?

Q 09 What is the difference between a linear equation in one and two variables?

Q 10 What does the term ‘solution’ mean for a linear equation in two variables?

Q 11 How is a linear equation plotted on a graph?

Q 12 What is the slope-intercept form of a linear equation?

Q 13 What is the role of the constant ‘c’ in ax+by+c=0?

Q 14 How are pairs of linear equations solved?

Q 15 Why does the chapter focus on pairs of equations?

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LINEAR EQUATIONS IN TWO VARIABLES — Learning Resources

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