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Practice Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions based on the NCERT syllabus. Solve fresh and exam-oriented MCQs on solutions, equations, graphs, intercepts, and coordinate concepts.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 5
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is an equation in which the highest power of each variable is 1. Its general form is:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
A linear equation in two variables has infinitely many solutions. Each solution can be represented by an ordered pair ((x,y)), and all these solutions together form a straight line when plotted on a coordinate plane.
This Practice Set 5 contains 5 fresh MCQs covering solutions, equations, intercepts, and graphical concepts.
What You Will Learn
✔ Finding solutions of linear equations
✔ Verifying ordered pairs
✔ Finding unknown coefficients
✔ Finding intercepts
✔ Understanding graphical representation
✔ Identifying equations from given conditions
Why This Topic Is Important
Linear equations in two variables help students understand relationships between two quantities. These concepts are important for algebra, coordinate geometry, and mathematical problem-solving.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ NCERT-Based Practice
✔ Mathematics Revision
Q1. If ((3,2)) is a solution of the equation
$$kx+2y=13,$$
then the value of (k) is:
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
B) (3)
Useful Concept
If an ordered pair is a solution of an equation, substituting its coordinates must satisfy the equation.
Solution
Given:
$$kx+2y=13$$
and the solution is:
$$(3,2)$$
Therefore:
$$x=3,\quad y=2$$
Substituting:
$$k(3)+2(2)=13$$
$$3k+4=13$$
Subtract 4 from both sides:
$$3k=9$$
Therefore:
$$k=3$$
Hence, the correct answer is:
B) (3)
Q2. Which of the following ordered pairs is not a solution of
$$x-2y=6?$$
A) ((6,0))
B) ((8,1))
C) ((10,2))
D) ((12,3))
Answer:
D) ((12,3))
Useful Concept
To check whether an ordered pair is a solution, substitute its coordinates into the given equation.
Solution
Given:
$$x-2y=6$$
Option A: ((6,0))
$$6-2(0)=6$$
Therefore, it is a solution.
Option B: ((8,1))
$$8-2(1)=8-2=6$$
Therefore, it is a solution.
Option C: ((10,2))
$$10-2(2)=10-4=6$$
Therefore, it is a solution.
Option D: ((12,3))
$$12-2(3)=12-6=6$$
This is also a solution.
Therefore, the original question would have no correct answer.
To make the MCQ valid, we correct option D.
Corrected Question
Which of the following ordered pairs is not a solution of:
$$x-2y=6?$$
A) ((6,0))
B) ((8,1))
C) ((10,2))
D) ((11,3))
Check D:
$$11-2(3)=11-6=5$$
Since:
$$5\ne6$$
((11,3)) is not a solution.
Therefore, the correct answer is:
D) ((11,3))
Q3. The (x)-intercept of the equation
$$3x+2y=12$$
is:
A) (2)
B) (3)
C) (4)
D) (6)
Answer:
C) (4)
Useful Concept
At the (x)-intercept, the value of (y) is zero.
Therefore:
$$y=0$$
Solution
Given:
$$3x+2y=12$$
For the (x)-intercept:
$$y=0$$
Substituting:
$$3x+2(0)=12$$
$$3x=12$$
Therefore:
$$x=4$$
Hence, the (x)-intercept is:
$$(4,0)$$
Therefore, the numerical value of the (x)-intercept is:
$$4$$
Hence, the correct answer is:
C) (4)
Q4. The (y)-intercept of the equation
$$4x+5y=20$$
is:
A) (2)
B) (4)
C) (5)
D) (20)
Answer:
B) (4)
Useful Concept
At the (y)-intercept:
$$x=0$$
Solution
Given:
$$4x+5y=20$$
For the (y)-intercept:
$$x=0$$
Substituting:
$$4(0)+5y=20$$
$$5y=20$$
Therefore:
$$y=4$$
Hence, the (y)-intercept is:
$$(0,4)$$
Therefore, the correct answer is:
B) (4)
Q5. Which of the following equations represents a line passing through the points ((0,5)) and ((5,0))?
A) (x+y=5)
B) (x-y=5)
C) (2x+y=5)
D) (x+2y=5)
Answer:
A) (x+y=5)
Useful Concept
A linear equation is satisfied by every point lying on its graph.
Solution
We need an equation satisfied by both:
$$(0,5)$$
and:
$$(5,0)$$
Check option A:
$$x+y=5$$
For ((0,5)):
$$0+5=5$$
Therefore, the point lies on the equation.
For ((5,0)):
$$5+0=5$$
Therefore, this point also lies on the equation.
Hence, the line:
$$x+y=5$$
passes through both given points.
Therefore, the correct answer is:
A) (x+y=5)
Important Concepts
Standard Form
A linear equation in two variables is generally written as:
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Solution
An ordered pair ((x,y)) is a solution if it satisfies the equation.
(x)-Intercept
To find the (x)-intercept:
$$y=0$$
(y)-Intercept
To find the (y)-intercept:
$$x=0$$
Graph
The graph of a linear equation in two variables is a straight line.
Example
For:
$$x+y=5$$
the intercepts are:
$$x\text{-intercept}=5$$
and:
$$y\text{-intercept}=5$$
Therefore, the line passes through:
$$(5,0)$$
and:
$$(0,5)$$
Related Practice Questions
Q1. Find the value of (k) if ((2,3)) is a solution of:
$$kx+y=11$$
Q2. Check whether ((4,1)) is a solution of:
$$2x+3y=11$$
Q3. Find the (x)-intercept of:
$$5x+y=15$$
Q4. Find the (y)-intercept of:
$$2x+3y=12$$
Q5. Write the equation of a line passing through ((0,6)) and ((6,0)).
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. If ((2,3)) satisfies:
$$kx+y=9,$$
find (k).
Q2. Find the (x)-intercept of:
$$2x+y=8$$
Q3. Find the (y)-intercept of:
$$x+4y=12$$
Q4. Does ((3,2)) satisfy:
$$x+2y=7?$$
Q5. Which equation passes through ((0,4)) and ((4,0))?
Exam Tips
✔ To find the (x)-intercept, put (y=0).
✔ To find the (y)-intercept, put (x=0).
✔ Always substitute both coordinates when checking a solution.
✔ If an unknown coefficient is given, substitute the known solution directly.
✔ Remember that all solutions of a linear equation lie on its straight-line graph.
✔ Check all MCQ options carefully before selecting the answer.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ (x)-intercept:
$$(x,0)$$
✔ (y)-intercept:
$$(0,y)$$
✔ At (x)-axis:
$$y=0$$
✔ At (y)-axis:
$$x=0$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Using (x=0) while finding the (x)-intercept.
❌ Using (y=0) while finding the (y)-intercept.
❌ Forgetting the negative sign in an ordered pair.
❌ Checking only one coordinate.
❌ Confusing an (x)-intercept with a (y)-intercept.
❌ Selecting an MCQ answer without verifying it in the original equation.
Key Takeaways
✔ A linear equation in two variables has infinitely many solutions.
✔ Every solution can be represented by an ordered pair.
✔ The (x)-intercept is obtained by putting (y=0).
✔ The (y)-intercept is obtained by putting (x=0).
✔ Two points satisfying the same linear equation lie on its graph.
✔ The graph of a linear equation in two variables is a straight line.
FAQs
Q. What is the (x)-intercept?
Answer:
The (x)-intercept is the point where the graph meets the (x)-axis. At this point:
$$y=0$$
Q. What is the (y)-intercept?
Answer:
The (y)-intercept is the point where the graph meets the (y)-axis. At this point:
$$x=0$$
Q. How can we find an unknown coefficient?
Answer:
Substitute the given solution into the equation and solve for the unknown coefficient.
Q. How many solutions does a linear equation in two variables have?
Answer:
A linear equation in two variables generally has infinitely many solutions.
Q. What is the graph of a linear equation in two variables?
Answer:
The graph is a straight line.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide fresh NCERT-based practice on solutions, coefficients, intercepts, and equations passing through given points.
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