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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 MCQs on solutions, equations, variables, axes, and graphical representation.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 3
Difficulty Level: Moderate
Based On: NCERT Latest Syllabus
Introduction
A linear equation in two variables is an equation containing two variables whose highest power 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 solution of a linear equation in two variables is an ordered pair ((x,y)) that satisfies the equation. The graph of such an equation is a straight line.
This Practice Set 3 contains 5 fresh MCQs focusing on finding solutions, determining unknown values, identifying points on axes, and understanding the graphical representation of linear equations.
What You Will Learn
✔ Finding solutions of linear equations
✔ Verifying ordered pairs
✔ Finding unknown values
✔ Points on coordinate axes
✔ Graphical representation
✔ Infinite solutions
✔ Relationship between two variables
Why This Topic Is Important
Linear equations in two variables help students understand the relationship between two quantities. The chapter provides an important foundation for coordinate geometry and algebraic 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. Which of the following is a solution of the equation
$$x+3y=11?$$
A) ((2,3))
B) ((5,2))
C) ((8,1))
D) ((1,4))
Answer:
A) ((2,3))
Useful Concept
An ordered pair ((x,y)) is a solution if it satisfies the given equation.
Solution
Given:
$$x+3y=11$$
For option A:
$$x=2,\quad y=3$$
Substituting:
$$2+3(3)=2+9=11$$
Therefore:
$$11=11$$
Hence, ((2,3)) is a solution.
Checking the other options:
For ((5,2)):
$$5+3(2)=11$$
This also gives:
$$11=11$$
Therefore, ((5,2)) is also a solution.
So the original options contain two correct answers. To keep the MCQ 100% valid with only one correct option, we correct the question.
Corrected Question
Which of the following is a solution of:
$$x+3y=12?$$
A) ((3,3))
B) ((6,2))
C) ((9,1))
D) ((0,3))
Check:
For ((3,3)):
$$3+3(3)=3+9=12$$
For ((6,2)):
$$6+3(2)=12$$
Again, two solutions.
Therefore, we need a cleaner set of options.
Final Correct Version
Which of the following ordered pairs is a solution of:
$$2x+3y=13?$$
A) ((2,3))
B) ((3,2))
C) ((4,2))
D) ((5,1))
For A:
$$2(2)+3(3)=4+9=13$$
For B:
$$2(3)+3(2)=6+6=12$$
For C:
$$2(4)+3(2)=8+6=14$$
For D:
$$2(5)+3(1)=10+3=13$$
Again, D also works.
So instead, use:
Final MCQ
Which of the following ordered pairs is a solution of:
$$2x+3y=14?$$
A) ((1,4))
B) ((2,3))
C) ((4,2))
D) ((5,1))
Checking:
A:
$$2(1)+3(4)=2+12=14$$
B:
$$2(2)+3(3)=4+9=13$$
C:
$$2(4)+3(2)=8+6=14$$
D:
$$10+3=13$$
Again two answers.
To avoid any ambiguity, the final verified MCQ is:
Q1. Which of the following ordered pairs is a solution of
$$2x+3y=14?$$
A) ((1,4))
B) ((2,4))
C) ((3,2))
D) ((5,1))
Check A:
$$2(1)+3(4)=2+12=14$$
Check B:
$$4+12=16$$
Check C:
$$6+6=12$$
Check D:
$$10+3=13$$
Therefore, the correct answer is:
A) ((1,4))
Q2. If the point ((4,y)) lies on the equation
$$2x+y=13,$$
then the value of (y) is:
A) (3)
B) (4)
C) (5)
D) (6)
Answer:
C) (5)
Useful Concept
When one coordinate is known, substitute it into the equation to find the other coordinate.
Solution
Given:
$$2x+y=13$$
The point is:
$$(4,y)$$
Therefore:
$$x=4$$
Substituting:
$$2(4)+y=13$$
$$8+y=13$$
Subtracting 8 from both sides:
$$y=5$$
Therefore, the point is:
$$(4,5)$$
Hence, the correct answer is:
C) (5)
Q3. Which point represents the (y)-intercept of the equation
$$3x+2y=12?$$
A) ((4,0))
B) ((0,6))
C) ((6,0))
D) ((0,4))
Answer:
B) ((0,6))
Useful Concept
To find the (y)-intercept, put:
$$x=0$$
because every point on the (y)-axis has (x=0).
Solution
Given:
$$3x+2y=12$$
For the (y)-intercept:
$$x=0$$
Therefore:
$$3(0)+2y=12$$
$$2y=12$$
Hence:
$$y=6$$
Therefore, the (y)-intercept is:
$$(0,6)$$
Hence, the correct answer is:
B) ((0,6))
Q4. Which of the following equations has ((2,3)) as a solution?
A) (x+y=4)
B) (2x+y=7)
C) (x+2y=5)
D) (3x+y=8)
Answer:
B) (2x+y=7)
Useful Concept
Substitute (x=2) and (y=3) into each equation to determine which equation is satisfied.
Solution
Given point:
$$(2,3)$$
Therefore:
$$x=2,\quad y=3$$
Check option A:
$$x+y=2+3=5$$
But:
$$5\ne4$$
So A is incorrect.
Check option B:
$$2x+y=2(2)+3$$
$$=4+3$$
$$=7$$
Therefore, the point satisfies this equation.
Check option C:
$$x+2y=2+2(3)=8$$
But:
$$8\ne5$$
Check option D:
$$3x+y=3(2)+3=9$$
But:
$$9\ne8$$
Therefore, the correct answer is:
B) (2x+y=7)
Q5. The equation
$$x=5$$
represents which type of graph?
A) A line parallel to the (x)-axis
B) A line parallel to the (y)-axis
C) The (x)-axis
D) The (y)-axis
Answer:
B) A line parallel to the (y)-axis
Useful Concept
An equation of the form:
$$x=a$$
represents a vertical line parallel to the (y)-axis.
Solution
Given:
$$x=5$$
Here, the value of (x) remains fixed at 5, while (y) can take any real value.
Some points satisfying the equation are:
$$(5,0)$$
$$(5,1)$$
$$(5,2)$$
$$(5,-1)$$
All these points have the same (x)-coordinate.
Therefore, they form a vertical straight line passing through:
$$(5,0)$$
This line is parallel to the (y)-axis.
Hence, the correct answer is:
B) A line parallel to the (y)-axis
Important Concepts
General Form
$$ax+by+c=0$$
where (a) and (b) are not both zero.
Solution
An ordered pair ((x,y)) that satisfies the equation is called its solution.
(x)-Intercept
To find the (x)-intercept, put:
$$y=0$$
(y)-Intercept
To find the (y)-intercept, put:
$$x=0$$
Equation (x=a)
The equation:
$$x=a$$
represents a line parallel to the (y)-axis.
Equation (y=b)
The equation:
$$y=b$$
represents a line parallel to the (x)-axis.
Graph
The graph of a linear equation in two variables is a straight line.
Related Practice Questions
Q1. Find the (x)-intercept of:
$$2x+y=8$$
Q2. Find the (y)-intercept of:
$$x+3y=12$$
Q3. Check whether ((3,4)) is a solution of:
$$2x+y=10$$
Q4. Find (y) when (x=5) in:
$$x+2y=11$$
Q5. What type of line is represented by:
$$y=4?$$
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. Find the (x)-intercept of:
$$x+y=9$$
Q2. Find the (y)-intercept of:
$$2x+y=6$$
Q3. Is ((2,5)) a solution of:
$$x+y=7?$$
Q4. What type of line does (x=3) represent?
Q5. What type of line does (y=6) represent?
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.
✔ Remember that (x=a) represents a vertical line.
✔ Remember that (y=b) represents a horizontal line.
✔ Keep the order of coordinates as ((x,y)).
✔ Carefully check signs while substituting values.
Quick Revision Notes
✔ General form:
$$ax+by+c=0$$
✔ (x)-intercept:
$$y=0$$
✔ (y)-intercept:
$$x=0$$
✔ Equation:
$$x=a$$
represents a line parallel to the (y)-axis.
✔ Equation:
$$y=b$$
represents a line parallel to the (x)-axis.
✔ Graph of a linear equation:
Straight line
Common Mistakes Students Make
❌ Putting (x=0) while finding the (x)-intercept.
❌ Putting (y=0) while finding the (y)-intercept.
❌ Confusing vertical and horizontal lines.
❌ Interchanging (x) and (y) coordinates.
❌ Checking only one part of an equation.
❌ Ignoring negative signs during substitution.
Key Takeaways
✔ A solution of a linear equation is an ordered pair.
✔ The (x)-intercept is obtained by putting (y=0).
✔ The (y)-intercept is obtained by putting (x=0).
✔ (x=a) represents a line parallel to the (y)-axis.
✔ (y=b) represents a line parallel to the (x)-axis.
✔ A linear equation in two variables has a straight-line graph.
FAQs
Q. How do we find the (x)-intercept?
Answer:
Put:
$$y=0$$
in the equation and find the value of (x).
Q. How do we find the (y)-intercept?
Answer:
Put:
$$x=0$$
in the equation and find the value of (y).
Q. What does (x=5) represent?
Answer:
It represents a vertical line parallel to the (y)-axis.
Q. What does (y=5) represent?
Answer:
It represents a horizontal line parallel to the (x)-axis.
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 solutions, intercepts, coordinate axes, and graphical representation.
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