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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 exam-oriented MCQs on solutions, equations, intercepts, graphs, and algebraic 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: 7
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is an equation in which the highest power of each variable is one. It can be written in the general form:
$$ax+by+c=0$$
where (a), (b), and (c) are real numbers and (a) and (b) are not both zero.
A solution of a linear equation in two variables is an ordered pair ((x,y)) that satisfies the equation. Since a linear equation in two variables generally has infinitely many solutions, its graph is a straight line.
This Practice Set 7 contains 5 fresh MCQs focusing on algebraic reasoning, solutions, intercepts, and graphical interpretation.
What You Will Learn
✔ Finding unknown values
✔ Verifying solutions
✔ Finding intercepts
✔ Understanding equations of lines
✔ Identifying graphical relationships
✔ Applying substitution
✔ Working with ordered pairs
Why This Topic Is Important
Linear equations in two variables are an important foundation for algebra and coordinate geometry. They help students understand relationships between two quantities and develop systematic problem-solving skills.
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 ((4,-1)) is a solution of the equation
$$kx+3y=13,$$
then the value of (k) is:
A) (3)
B) (4)
C) (5)
D) (6)
Answer:
C) (4)
Useful Concept
If an ordered pair is a solution of an equation, substituting its coordinates must satisfy the equation.
Solution
Given:
$$kx+3y=13$$
The solution is:
$$(4,-1)$$
Therefore:
$$x=4,\quad y=-1$$
Substituting:
$$k(4)+3(-1)=13$$
$$4k-3=13$$
Add 3 to both sides:
$$4k=16$$
Therefore:
$$k=4$$
Hence, the correct answer is:
B) (4)
Correction: The numerical answer is (4), so the correct option is B, not C.
Q2. Which of the following ordered pairs is a solution of
$$5x-2y=16?$$
A) ((2,-3))
B) ((2,1))
C) ((4,2))
D) ((0,-8))
Answer:
A) ((2,-3))
Useful Concept
Substitute the coordinates of each ordered pair into the equation to check whether it is a solution.
Solution
Given:
$$5x-2y=16$$
For option A:
$$x=2,\quad y=-3$$
Substituting:
$$5(2)-2(-3)$$
$$=10+6$$
$$=16$$
Therefore, ((2,-3)) is a solution.
Check the other options:
For ((2,1)):
$$5(2)-2(1)=10-2=8\ne16$$
For ((4,2)):
$$5(4)-2(2)=20-4=16$$
This is also a solution.
Therefore, the original options contain two correct answers.
Corrected Q2
Which of the following ordered pairs is a solution of:
$$5x-2y=16?$$
A) ((2,-3))
B) ((2,1))
C) ((4,3))
D) ((1,-2))
Check A:
$$10+6=16$$
Check B:
$$10-2=8$$
Check C:
$$20-6=14$$
Check D:
$$5+4=9$$
Therefore, the correct answer is:
A) ((2,-3))
Q3. The (x)-intercept of the equation
$$4x+3y=24$$
is:
A) (4)
B) (6)
C) (8)
D) (12)
Answer:
B) (6)
Useful Concept
At the (x)-intercept, the point lies on the (x)-axis. Therefore:
$$y=0$$
Solution
Given:
$$4x+3y=24$$
Put:
$$y=0$$
Then:
$$4x+3(0)=24$$
$$4x=24$$
Therefore:
$$x=6$$
Hence, the (x)-intercept is:
$$(6,0)$$
Therefore, the correct answer is:
B) (6)
Q4. If the equation
$$2x+3y=12$$
is satisfied by the point ((x,2)), then the value of (x) is:
A) (2)
B) (3)
C) (4)
D) (5)
Answer:
C) (3)
Useful Concept
When one coordinate is given, substitute it into the equation and solve for the unknown coordinate.
Solution
Given:
$$2x+3y=12$$
The point is:
$$(x,2)$$
Therefore:
$$y=2$$
Substitute (y=2):
$$2x+3(2)=12$$
$$2x+6=12$$
Subtract 6:
$$2x=6$$
Therefore:
$$x=3$$
Hence, the corresponding point is:
$$(3,2)$$
Therefore, the correct answer is:
B) (3)
Correction: The numerical answer is (3), so the correct option is B, not C.
Q5. Which of the following statements is correct for the equation
$$x+y=6?$$
A) It has only one solution.
B) It has exactly two solutions.
C) It has infinitely many solutions.
D) It has no solution.
Answer:
C) It has infinitely many solutions.
Useful Concept
A linear equation in two variables generally has infinitely many solutions.
Solution
Given:
$$x+y=6$$
Choose different values of (x) and calculate the corresponding value of (y).
If:
$$x=0$$
then:
$$y=6$$
So:
$$(0,6)$$
is a solution.
If:
$$x=2$$
then:
$$y=4$$
So:
$$(2,4)$$
is a solution.
If:
$$x=5$$
then:
$$y=1$$
So:
$$(5,1)$$
is a solution.
If:
$$x=10$$
then:
$$y=-4$$
So:
$$(10,-4)$$
is also a solution.
Since we can choose infinitely many values of (x), there are infinitely many corresponding values of (y).
Therefore, the equation has infinitely many solutions.
Hence, the correct answer is:
C) It has infinitely many solutions.
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
For the (x)-intercept:
$$y=0$$
(y)-Intercept
For the (y)-intercept:
$$x=0$$
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 ((3,4)) is a solution of:
$$kx+y=13,$$
find (k).
Q2. Check whether ((2,5)) is a solution of:
$$3x+y=11$$
Q3. Find the (x)-intercept of:
$$5x+2y=20$$
Q4. Find the (y)-intercept of:
$$3x+4y=12$$
Q5. Write any three solutions of:
$$x+y=8$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. If ((2,3)) satisfies:
$$kx+2y=10,$$
find (k).
Q2. Find the (x)-intercept of:
$$3x+y=12$$
Q3. Find the (y)-intercept of:
$$2x+5y=20$$
Q4. Is ((4,2)) a solution of:
$$x+2y=8?$$
Q5. How many solutions does a linear equation in two variables generally have?
Exam Tips
✔ Substitute the given coordinates carefully.
✔ Remember that negative signs are part of the values.
✔ For the (x)-intercept, put (y=0).
✔ For the (y)-intercept, put (x=0).
✔ A linear equation in two variables generally has infinitely many solutions.
✔ Verify your final answer in the original equation whenever possible.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ Solution:
$$(x,y)$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Number of solutions:
Infinitely many
✔ Graph:
Straight line
Common Mistakes Students Make
❌ Forgetting the negative sign while substituting.
❌ Confusing the (x)-intercept with the (y)-intercept.
❌ Assuming that a linear equation in two variables has only one solution.
❌ Interchanging (x) and (y) coordinates.
❌ Not checking the final value in the original equation.
Key Takeaways
✔ A linear equation in two variables can be represented as:
$$ax+by+c=0$$
✔ Its solutions are ordered pairs.
✔ A linear equation in two variables generally has infinitely many solutions.
✔ The (x)-intercept is found by putting (y=0).
✔ The (y)-intercept is found by putting (x=0).
✔ Its graph is a straight line.
FAQs
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. How can we check an ordered pair?
Answer:
Substitute the values of (x) and (y) into the equation. If the equation is satisfied, the ordered pair is a solution.
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. What is the graph of a linear equation in two variables?
Answer:
Its 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 unknown coefficients, ordered pairs, intercepts, and the number of solutions of a linear equation.
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