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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 linear equations, solutions, graphs, ordered pairs, 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: 1
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction
Linear Equations in Two Variables is an important chapter in Class 9 Mathematics. In this chapter, students learn how to represent relationships between two variables using linear equations.
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.
Students also learn how to find solutions of linear equations, represent solutions as ordered pairs, and understand their graphical representation.
This practice set contains 5 fresh MCQs covering important concepts related to linear equations in two variables.
What You Will Learn
✔ Linear equations in two variables
✔ Standard form of a linear equation
✔ Ordered pairs
✔ Solutions of linear equations
✔ Checking whether an ordered pair is a solution
✔ Finding unknown values
✔ Graphical representation of linear equations
✔ Number of solutions of a linear equation
Why This Topic Is Important
Linear equations in two variables form an important foundation for coordinate geometry and algebra.
Understanding how to find and verify solutions helps students solve problems involving two unknown quantities. The concepts are also useful in graphical methods and higher classes.
Exam Relevance
These questions are useful for:
✔ CBSE Board Preparation
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Mathematics Revision
✔ NCERT-Based Practice
Q1. Which of the following is a linear equation in two variables?
A) (x^2+y=5)
B) (2x+3y=7)
C) (xy=6)
D) (x^2+y^2=9)
Answer:
B) (2x+3y=7)
Useful Concept
A linear equation in two variables can be written in the form:
$$ax+by+c=0$$
where the powers of (x) and (y) are both 1.
Solution
Consider the given options.
Option A:
$$x^2+y=5$$
Here, the power of (x) is 2. Therefore, it is not a linear equation.
Option B:
$$2x+3y=7$$
Rearranging:
$$2x+3y-7=0$$
This is of the form:
$$ax+by+c=0$$
Therefore, it is a linear equation in two variables.
Option C:
$$xy=6$$
The variables are multiplied together, so it is not a linear equation.
Option D:
$$x^2+y^2=9$$
The variables have powers 2, so it is not a linear equation.
Therefore, the correct answer is:
B) (2x+3y=7)
Q2. Which of the following ordered pairs is a solution of the equation
$$2x+y=7?$$
A) ((1,4))
B) ((2,3))
C) ((3,1))
D) ((4,1))
Answer:
B) ((2,3))
Useful Concept
An ordered pair ((x,y)) is a solution of a linear equation if its values satisfy the equation after substitution.
Solution
Given:
$$2x+y=7$$
We check each option.
Option A: ((1,4))
Put (x=1) and (y=4):
$$2(1)+4=6$$
But:
$$6\ne7$$
So, ((1,4)) is not a solution.
Option B: ((2,3))
Put (x=2) and (y=3):
$$2(2)+3=4+3=7$$
Therefore:
$$2x+y=7$$
So, ((2,3)) is a solution.
Option C: ((3,1))
$$2(3)+1=7$$
This also gives:
$$7=7$$
Therefore, ((3,1)) is also a solution.
This means the question as originally framed has two correct options, B and C.
To make the MCQ valid with only one correct answer, the options should be corrected.
Corrected Question
Which of the following ordered pairs is a solution of:
$$2x+y=8?$$
A) ((1,4))
B) ((2,3))
C) ((3,1))
D) ((4,1))
For ((2,3)):
$$2(2)+3=7\ne8$$
For ((1,4)):
$$2(1)+4=6\ne8$$
For ((3,1)):
$$2(3)+1=7\ne8$$
For ((4,1)):
$$2(4)+1=9\ne8$$
Again, none works. So the cleanest corrected version is:
Final Correct Question
Which of the following ordered pairs is a solution of:
$$2x+y=7?$$
A) ((1,3))
B) ((2,3))
C) ((3,2))
D) ((4,2))
Checking B:
$$2(2)+3=7$$
Therefore, the correct answer is:
B) ((2,3))
Q3. If (x=3) is a solution of the equation
$$x+2y=9,$$
then what is the value of (y)?
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
B) (3)
Useful Concept
When one variable is known, substitute its value into the equation and solve for the other variable.
Solution
Given:
$$x+2y=9$$
and:
$$x=3$$
Substituting (x=3):
$$3+2y=9$$
Subtract 3 from both sides:
$$2y=6$$
Therefore:
$$y=3$$
Hence, the required ordered pair is:
$$(3,3)$$
Therefore, the correct answer is:
B) (3)
Q4. How many solutions does the linear equation
$$3x-2y=6$$
have?
A) No solution
B) One solution
C) Two solutions
D) Infinitely many solutions
Answer:
D) Infinitely many solutions
Useful Concept
A linear equation in two variables generally has infinitely many solutions.
Each solution can be represented by an ordered pair ((x,y)).
Solution
Given:
$$3x-2y=6$$
We can express (y) in terms of (x):
$$-2y=6-3x$$
Therefore:
$$2y=3x-6$$
So:
$$y=\frac{3x-6}{2}$$
For different values of (x), we obtain different values of (y).
For example:
If:
$$x=2$$
then:
$$y=\frac{6-6}{2}=0$$
So one solution is:
$$(2,0)$$
If:
$$x=0$$
then:
$$y=\frac{-6}{2}=-3$$
So another solution is:
$$(0,-3)$$
Since we can choose infinitely many values of (x), the equation has infinitely many ordered-pair solutions.
Therefore, the correct answer is:
D) Infinitely many solutions
Q5. The point ((0,5)) lies on the graph of which of the following equations?
A) (x+y=5)
B) (2x+y=10)
C) (x-y=5)
D) (3x+y=10)
Answer:
A) (x+y=5)
Useful Concept
To check whether a point lies on the graph of an equation, substitute the coordinates of the point into the equation.
For the point:
$$(0,5)$$
we have:
$$x=0,\quad y=5$$
Solution
Option A
$$x+y=5$$
Substituting:
$$0+5=5$$
Therefore:
$$5=5$$
Hence, the point satisfies the equation.
Option B
$$2x+y=10$$
$$2(0)+5=5\ne10$$
Not correct.
Option C
$$x-y=5$$
$$0-5=-5\ne5$$
Not correct.
Option D
$$3x+y=10$$
$$3(0)+5=5\ne10$$
Not correct.
Therefore, the correct answer is:
A) (x+y=5)
Important Concepts
Standard Form
A linear equation in two variables can be written as:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
Solution of a Linear Equation
An ordered pair:
$$(x,y)$$
is called a solution of a linear equation if it satisfies the equation.
Example
For:
$$x+y=7$$
the ordered pair:
$$(3,4)$$
is a solution because:
$$3+4=7$$
Infinite Solutions
A linear equation in two variables generally has infinitely many solutions.
For example:
$$x+y=5$$
has solutions:
$$(0,5),(1,4),(2,3),(3,2),(4,1),(5,0)$$
and many more.
Graphical Representation
The graph of a linear equation in two variables is a straight line.
Ordered Pair
An ordered pair is written as:
$$(x,y)$$
The first coordinate represents the value of (x), while the second coordinate represents the value of (y).
Related Practice Questions
Q1. Which of the following is a linear equation in two variables?
$$3x+4y=12$$
Q2. Check whether ((2,5)) is a solution of:
$$x+2y=12$$
Q3. Find the value of (y) if (x=4) in:
$$2x+y=11$$
Q4. Write any three solutions of:
$$x+y=6$$
Q5. Does the point ((3,2)) lie on the graph of:
$$x+y=5?$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Which ordered pair satisfies:
$$x+y=9?$$
A) ((3,5))
B) ((4,5))
C) ((2,6))
D) ((1,7))
Q2. Find (y) when (x=2) in:
$$3x+y=11$$
Q3. How many solutions does a linear equation in two variables generally have?
Q4. Does ((0,4)) satisfy:
$$2x+y=4?$$
Q5. What type of graph represents a linear equation in two variables?
Exam Tips
✔ Always identify the variables before solving the equation.
✔ When checking an ordered pair, substitute both coordinates carefully.
✔ Remember that the order in ((x,y)) is important.
✔ A linear equation in two variables generally has infinitely many solutions.
✔ The graph of a linear equation in two variables is a straight line.
✔ Avoid confusing a linear equation with equations containing (x^2), (y^2), or (xy).
✔ In MCQs, substitute the given values directly whenever possible.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ A solution is represented by an ordered pair:
$$(x,y)$$
✔ A linear equation in two variables generally has:
Infinitely many solutions
✔ The graph of a linear equation in two variables is:
A straight line
✔ To verify a solution, substitute the values of (x) and (y) into the equation.
✔ In an ordered pair ((x,y)):
- (x) = first coordinate
- (y) = second coordinate
Common Mistakes Students Make
❌ Treating (x^2+y=5) as a linear equation.
❌ Forgetting that (xy) makes an equation non-linear.
❌ Interchanging (x) and (y) in an ordered pair.
❌ Checking only one coordinate instead of substituting both.
❌ Assuming that a linear equation in two variables has only one solution.
❌ Making arithmetic mistakes while substituting values.
❌ Forgetting that the graph of a linear equation in two variables is a straight line.
Key Takeaways
✔ A linear equation in two variables has the form:
$$ax+by+c=0$$
✔ Its solution is represented by an ordered pair.
✔ A pair of values is a solution only when it satisfies the equation.
✔ A linear equation in two variables generally has infinitely many solutions.
✔ The graph of a linear equation in two variables is a straight line.
✔ Substitution is an easy method to verify whether an ordered pair is a solution.
FAQs
Q. What is a linear equation in two variables?
Answer:
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 not both zero.
Q. What is a solution of a linear equation in two variables?
Answer:
An ordered pair ((x,y)) is called a solution if its values satisfy the given equation.
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 of a linear equation in two variables is a straight line.
Q. How can we check whether an ordered pair is a solution?
Answer:
Substitute the values of (x) and (y) from the ordered pair into the equation. If the equation is satisfied, the ordered pair is a solution.
Conclusion
These Class 9 Maths Chapter 4 Linear Equations in Two Variables MCQ Questions with Answers and Solutions -provide NCERT-based practice on linear equations, ordered pairs, solutions, and graphical concepts.
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