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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, coefficients, intercepts, graphs, and linear equations.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 10
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is generally written in the form:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
An ordered pair ((x,y)) is called a solution of the equation if it satisfies the equation. A linear equation in two variables generally has infinitely many solutions, and its graph is a straight line.
This Practice Set 10 contains 5 fresh MCQs focusing on algebraic reasoning, solutions, intercepts, equations of lines, and graphical concepts.
What You Will Learn
✔ Finding unknown coefficients
✔ Verifying ordered pairs
✔ Finding (x)- and (y)-intercepts
✔ Constructing equations from given conditions
✔ Understanding graphs of linear equations
✔ Applying substitution and logical reasoning
Why This Topic Is Important
Linear equations in two variables form an important foundation for algebra and coordinate geometry. They help students understand relationships between two quantities and prepare them for more advanced mathematical concepts.
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 the point ((3,-2)) lies on the equation
$$kx+4y=7,$$
then the value of (k) is:
A) (3)
B) (4)
C) (5)
D) (6)
Answer:
C) (5)
Useful Concept
If a point lies on the graph of an equation, its coordinates satisfy the equation.
Solution
Given:
$$kx+4y=7$$
The point is:
$$(3,-2)$$
Therefore:
$$x=3,\quad y=-2$$
Substitute:
$$3k+4(-2)=7$$
$$3k-8=7$$
Adding 8:
$$3k=15$$
Therefore:
$$k=5$$
Hence, the correct answer is:
C) (5)
Q2. Which of the following ordered pairs is not a solution of
$$3x-2y=8?$$
A) ((2,-1))
B) ((4,2))
C) ((0,-4))
D) ((6,5))
Answer:
D) ((6,5))
Useful Concept
An ordered pair is a solution only when its substitution satisfies the given equation.
Solution
Given:
$$3x-2y=8$$
Option A: ((2,-1))
$$3(2)-2(-1)=6+2=8$$
So it is a solution.
Option B: ((4,2))
$$3(4)-2(2)=12-4=8$$
So it is a solution.
Option C: ((0,-4))
$$3(0)-2(-4)=0+8=8$$
So it is a solution.
Option D: ((6,5))
$$3(6)-2(5)=18-10=8$$
This is also a solution.
Therefore, the options contain no incorrect pair.
To keep the MCQ 100% correct, we replace option D with ((6,4)).
Final Verified Q2
Which of the following ordered pairs is not a solution of:
$$3x-2y=8?$$
A) ((2,-1))
B) ((4,2))
C) ((0,-4))
D) ((6,4))
For D:
$$3(6)-2(4)=18-8=10$$
Since:
$$10\ne8$$
((6,4)) is not a solution.
Therefore, the correct answer is:
D) ((6,4))
Q3. The (x)-intercept and (y)-intercept of the equation
$$2x+3y=12$$
are respectively:
A) (6) and (4)
B) (4) and (6)
C) (12) and (12)
D) (3) and (2)
Answer:
A) (6) and (4)
Useful Concept
For the (x)-intercept:
$$y=0$$
For the (y)-intercept:
$$x=0$$
Solution
Given:
$$2x+3y=12$$
Finding the (x)-intercept
Put:
$$y=0$$
Then:
$$2x=12$$
Therefore:
$$x=6$$
So:
$$x\text{-intercept}=6$$
Finding the (y)-intercept
Put:
$$x=0$$
Then:
$$3y=12$$
Therefore:
$$y=4$$
So:
$$y\text{-intercept}=4$$
Hence, the correct answer is:
A) (6) and (4)
Q4. Which of the following equations represents a line passing through the points ((2,1)) and ((4,5))?
A) (2x-y=3)
B) (2x+y=5)
C) (x-2y=0)
D) (x+y=3)
Answer:
A) (2x-y=3)
Useful Concept
The equation of the required line must be satisfied by both given points.
Solution
Given points:
$$(2,1)$$
and:
$$(4,5)$$
Check option A:
$$2x-y=3$$
For ((2,1)):
$$2(2)-1=4-1=3$$
So the first point satisfies the equation.
For ((4,5)):
$$2(4)-5=8-5=3$$
So the second point also satisfies the equation.
Therefore, both points lie on:
$$2x-y=3$$
Hence, the correct answer is:
A) (2x-y=3)
Q5. If the equation
$$5x-2y=20$$
has (y=5), then the corresponding value of (x) is:
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
C) (6)
Useful Concept
Substitute the given value of one variable into the equation and solve for the other variable.
Solution
Given:
$$5x-2y=20$$
and:
$$y=5$$
Substitute:
$$5x-2(5)=20$$
$$5x-10=20$$
Add 10:
$$5x=30$$
Therefore:
$$x=6$$
Hence, the corresponding point is:
$$(6,5)$$
Therefore, the numerical answer is:
$$6$$
Corrected Options
A) (3)
B) (4)
C) (5)
D) (6)
Hence, the correct answer is:
D) (6)
Important Concepts
Standard Form
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Solution
An ordered pair ((x,y)) satisfying the equation is called a solution.
(x)-Intercept
Put:
$$y=0$$
(y)-Intercept
Put:
$$x=0$$
Vertical Line
$$x=a$$
represents a line parallel to the (y)-axis.
Horizontal Line
$$y=b$$
represents a line parallel to the (x)-axis.
Number of Solutions
A linear equation in two variables generally has infinitely many solutions.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. If ((2,-3)) is a solution of:
$$kx+2y=8,$$
find (k).
Q2. Check whether ((5,1)) satisfies:
$$2x-3y=7$$
Q3. Find both intercepts of:
$$3x+2y=12$$
Q4. Which equation passes through ((0,5)) and ((5,0))?
Q5. Find the value of (y) if (x=4) in:
$$3x+2y=14$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. If ((2,3)) is a solution of:
$$kx+y=11,$$
find (k).
Q2. Find the (x)-intercept of:
$$4x+3y=12$$
Q3. Find the (y)-intercept of:
$$2x+5y=20$$
Q4. Which equation represents a vertical line?
A) (y=4)
B) (x=4)
C) (x+y=4)
D) (2x+y=4)
Q5. Find (y) when (x=2) in:
$$3x+y=11$$
Exam Tips
✔ Always substitute the given coordinates carefully.
✔ For an (x)-intercept, set (y=0).
✔ For a (y)-intercept, set (x=0).
✔ When constructing an equation from points, verify both points.
✔ Remember that (x=a) represents a vertical line.
✔ Remember that (y=b) represents a horizontal line.
✔ Always check the final value in the original equation.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Vertical line:
$$x=a$$
✔ Horizontal line:
$$y=b$$
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Forgetting the negative sign while substituting.
❌ Confusing (x)-intercept with (y)-intercept.
❌ Assuming (x=a) represents a horizontal line.
❌ Not checking both given points when identifying an equation.
❌ Making arithmetic errors while simplifying.
❌ Selecting an answer without verifying it in the original equation.
Key Takeaways
✔ A linear equation in two variables has the general form:
$$ax+by+c=0$$
✔ Every solution is an ordered pair.
✔ A linear equation in two variables generally has infinitely many solutions.
✔ Its graph is a straight line.
✔ (x=a) represents a vertical line.
✔ (y=b) represents a horizontal line.
✔ Intercepts can be found by setting one variable equal to zero.
FAQs
Q. How do we find the (x)-intercept?
Answer:
Put:
$$y=0$$
and solve for (x).
Q. How do we find the (y)-intercept?
Answer:
Put:
$$x=0$$
and solve for (y).
Q. How can we verify whether a point lies on a line?
Answer:
Substitute the coordinates of the point into the equation. If the equation is satisfied, the point lies on the line.
Q. What does (x=a) represent?
Answer:
It represents a vertical line parallel to the (y)-axis.
Q. What does (y=b) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions – provide fresh NCERT-based practice on unknown coefficients, ordered pairs, intercepts, equations of lines, and graphical concepts.
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