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Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers based on the latest NCERT syllabus. Solve unique MCQs on graphical method, substitution, elimination, cross multiplication, consistency, and word problems with detailed solutions for CBSE and state board exams.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
The chapter Pair of Linear Equations in Two Variables introduces students to solving two simultaneous equations using algebraic and graphical methods. Students also learn how to identify the nature of solutions and apply these concepts to solve practical problems involving age, money, distance, and other real-life situations. Regular MCQ practice strengthens conceptual understanding and prepares students for board examinations.
What You Will Learn?
✔ Standard Form of Linear Equations
✔ Graphical Method
✔ Elimination Method
✔ Substitution Method
✔ Cross Multiplication Method
✔ Consistency of Equations
✔ Real-Life Applications
✔ Board Exam Oriented Concepts
Why This Topic Is Important?
This chapter is one of the most scoring chapters in Class 10 Mathematics. It develops logical reasoning and problem-solving skills that are useful in algebra, coordinate geometry, economics, and everyday calculations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. The solution of the equations
$$x+y=6$$
$$3x-y=6$$
is:
A)
$$(2,4)$$
B)
$$(3,3)$$
C)
$$(4,2)$$
D)
$$(5,1)$$
Answer:
$$(3,3)$$
Useful Formula for this Question:
Add the equations to eliminate one variable.
Solution:
Given,
$$x+y=6$$
$$3x-y=6$$
Adding,
$$4x=12$$
$$x=3$$
Substitute into
$$x+y=6$$
$$3+y=6$$
$$y=3$$
Hence, the correct answer is:
$$(3,3)$$
Q2. Which method can be used to find the solution by drawing straight lines?
A) Substitution Method
B) Elimination Method
C) Graphical Method
D) Cross Multiplication Method
Answer:
Graphical Method
Useful Formula for this Question:
Each linear equation represents a straight line on the coordinate plane.
Solution:
In the graphical method, the equations are represented by straight lines, and the point of intersection gives the solution.
Hence, the correct answer is:
Graphical Method
Q3. If
$$7x+2y=20$$
and
$$x=2$$
then the value of
$$y$$
is:
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$3$$
Useful Formula for this Question:
Substitute the given value into the equation.
Solution:
Given,
$$7x+2y=20$$
Substitute
$$x=2$$
$$14+2y=20$$
$$2y=6$$
$$y=3$$
Hence, the correct answer is:
$$3$$
Q4. If
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
then the equations represent:
A) Parallel Lines
B) Intersecting Lines
C) Coincident Lines
D) Perpendicular Lines
Answer:
Coincident Lines
Useful Formula for this Question:
If
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
then the equations have infinitely many solutions.
Solution:
Equal ratios indicate that both equations represent the same straight line.
Hence, they are coincident lines and have infinitely many solutions.
Therefore, the correct answer is:
Coincident Lines
Q5. A father is 40 years old and his son is 15 years old. Let the present ages be represented by x and y, respectively. Which pair of equations correctly represents the situation?
A)
$$x+y=55,\quad x-y=25$$
B)
$$x+y=40,\quad x-y=15$$
C)
$$x+y=25,\quad x-y=55$$
D)
$$x+y=45,\quad x-y=20$$
Answer:
$$x+y=55,\quad x-y=25$$
Useful Formula for this Question:
For age-related problems,
Sum = Total Age
Difference = Age Difference
Solution:
Father’s age
$$=40$$
Son’s age
$$=15$$
Therefore,
$$x+y=40+15=55$$
and
$$x-y=40-15=25$$
Hence, the correct answer is:
$$x+y=55,\quad x-y=25$$
Important Formulas and Concepts
Standard Form
$$a_1x+b_1y+c_1=0$$
$$a_2x+b_2y+c_2=0$$
Unique Solution
$$\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$$
No Solution
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$$
Infinitely Many Solutions
$$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$$
Methods of Solving
✔ Graphical Method
✔ Substitution Method
✔ Elimination Method
✔ Cross Multiplication Method
FAQs
Q. What is the graphical solution of a pair of linear equations?
Answer:
The graphical solution is the point where the two straight lines intersect on the coordinate plane.
Q. What are coincident lines?
Answer:
Coincident lines are two lines that completely overlap each other and have infinitely many common points.
Q. Where are pair of linear equations used in daily life?
Answer:
They are used in solving problems related to age, money, distance, speed, mixtures, and business calculations.
Common Mistakes Students Make
❌ Forgetting to verify the solution in both equations.
❌ Confusing coincident and parallel lines.
❌ Making sign errors while eliminating variables.
❌ Using incorrect ratios to check consistency.
❌ Incorrectly forming equations from word problems.
Quick Revision Notes
✔ Every linear equation represents a straight line.
✔ Intersecting lines have one unique solution.
✔ Parallel lines have no solution.
✔ Coincident lines have infinitely many solutions.
✔ Graphical, Substitution, Elimination, and Cross Multiplication are the four standard solving methods.
✔ Word problems are solved by first forming two linear equations.
Conclusion:
These Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers and Solutions – contain fresh, unique, and NCERT-based questions without repetition. Regular practice of these board-oriented MCQs strengthens conceptual understanding, improves analytical thinking, and helps students score higher in CBSE board exams, state board exams, school tests, and scholarship examinations.
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