Welcome To My School Study
Practice Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQ Questions with Answers based on NCERT syllabus. Learn linear equations, variables, coefficients, constants, and standard form with detailed solutions, formulas, and board exam tips.
Do You Know
Chapter Information
Subject: Mathematics
Class: 10
Chapter: Pair of Linear Equations in Two Variables
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Board Exam Foundation Level
Based On: NCERT Latest Syllabus
Introduction:
Pair of Linear Equations in Two Variables is one of the most important chapters in Class 10 Mathematics. In Class 9, students learned about linear equations in one variable. In this chapter, we extend that knowledge to equations containing two variables, usually represented by $$x$$ and $$y$$.
A linear equation in two variables represents a straight line when plotted on a graph. When two such equations are considered together, they form a pair of linear equations. These equations help solve real-life problems involving age, money, speed, distance, profit, and many other situations.
Understanding the basics of variables, coefficients, constants, and the standard form of equations is essential before learning graphical and algebraic methods of solving them. This practice set focuses on these fundamental concepts and helps students build a strong foundation for the rest of the chapter.
What You Will Learn?
✔ Meaning of Linear Equations
✔ Two Variables in an Equation
✔ Coefficients
✔ Constants
✔ Standard Form of Linear Equations
✔ Basic Board Exam Concepts
Why This Topic Is Important?
This chapter forms the foundation for solving real-life mathematical problems and is frequently tested in school and board examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
————————————————–
Q1. Which of the following is a linear equation in two variables?
A) $$2x+3y=7$$
B) $$x^2+y=5$$
C) $$x+y^2=8$$
D) $$x^2+y^2=10$$
Answer:
$$2x+3y=7$$
Useful Formula for this Question:
Standard Linear Form:
$$ax+by+c=0$$
Concept Behind This Question:
The highest power of each variable in a linear equation must be:
$$1$$
Solution:
Option A:
$$2x+3y=7$$
Highest power of:
$$x=1$$
and
$$y=1$$
Therefore it is a linear equation.
Other options contain:
$$x^2$$
or
$$y^2$$
which makes them non-linear.
Therefore, the correct answer is:
$$2x+3y=7$$
Exam Tip:
A linear equation never contains squares, cubes, or higher powers of variables.
————————————————–
Q2. How many variables are present in:
$$4x-5y=12$$
A) $$1$$
B) $$2$$
C) $$3$$
D) $$4$$
Answer:
$$2$$
Useful Formula for this Question:
Variables are symbols whose values can change.
Concept Behind This Question:
Variables are usually represented by letters.
Solution:
Given equation:
$$4x-5y=12$$
Variables present are:
$$x$$
and
$$y$$
Therefore, total variables:
$$2$$
Hence, the correct answer is:
$$2$$
Exam Tip:
Numbers are constants; letters are variables.
————————————————–
Q3. What is the coefficient of:
$$x$$
in
$$7x+2y=10$$
A) $$2$$
B) $$7$$
C) $$10$$
D) $$1$$
Answer:
$$7$$
Useful Formula for this Question:
Coefficient = Number multiplied by the variable.
Concept Behind This Question:
The coefficient indicates how many times the variable is multiplied.
Solution:
Given equation:
$$7x+2y=10$$
The number multiplying:
$$x$$
is:
$$7$$
Therefore, coefficient of:
$$x$$
is:
$$7$$
Hence, the correct answer is:
$$7$$
Exam Tip:
Look immediately before the variable to find its coefficient.
————————————————–
Q4. Which of the following represents the standard form of a linear equation in two variables?
A) $$ax+by+c=0$$
B) $$ax^2+by+c=0$$
C) $$ax+by^2+c=0$$
D) $$ax^2+by^2+c=0$$
Answer:
$$ax+by+c=0$$
Useful Formula for this Question:
Standard Form:
$$ax+by+c=0$$
Concept Behind This Question:
Both variables must have degree:
$$1$$
Solution:
A linear equation in two variables is written as:
$$ax+by+c=0$$
where:
$$a,\ b,\ c$$
are constants and:
$$a\neq0,\ b\neq0$$
Therefore, the correct answer is:
$$ax+by+c=0$$
Exam Tip:
Memorize the standard form because it is used throughout the chapter.
————————————————–
Q5. In the equation:
$$3x+4y-9=0$$
the constant term is:
A) $$3$$
B) $$4$$
C) $$9$$
D) $$-9$$
Answer:
$$-9$$
Useful Formula for this Question:
Constant Term = Number without a variable.
Concept Behind This Question:
A constant remains fixed and does not contain any variable.
Solution:
Given equation:
$$3x+4y-9=0$$
Terms containing variables:
$$3x,\ 4y$$
Term without variable:
$$-9$$
Therefore, the constant term is:
$$-9$$
Hence, the correct answer is:
$$-9$$
Exam Tip:
The constant term never contains a variable.
————————————————–
Important Formulas and Concepts
Linear Equation in Two Variables:
$$ax+by+c=0$$
Variables:
$$x,\ y$$
Coefficient:
Number attached to a variable.
Constant:
A fixed numerical value without variables.
Condition:
$$a\neq0,\ b\neq0$$
————————————————–
FAQs
Q. What is a linear equation in two variables?
Answer:
An equation containing two variables whose highest powers are:
$$1$$
Q. Which variables are commonly used?
Answer:
Usually:
$$x$$
and
$$y$$
Q. Why is this chapter important?
Answer:
It helps solve practical problems involving two unknown quantities.
————————————————–
Common Mistakes Students Make
❌ Confusing coefficients with constants.
❌ Selecting equations containing:
$$x^2$$
or
$$y^2$$
as linear equations.
❌ Forgetting the standard form.
❌ Counting constants as variables.
————————————————–
Quick Revision Notes
✔ Linear Equation:
$$ax+by+c=0$$
✔ Variables:
$$x,\ y$$
✔ Coefficient = Number multiplied by variable.
✔ Constant = Number without variable.
✔ Highest power of each variable must be:
$$1$$
————————————————–
Conclusion:
These Class 10 Maths Chapter 3 MCQs introduce the basic concepts of Pair of Linear Equations in Two Variables. A strong understanding of variables, coefficients, constants, and standard form will make it easier to learn graphical and algebraic methods in the upcoming practice sets.
Related links
- Class 10 Maths Chapter 2 Polynomials (Graphical Zeroes) – Part 13
- Class 10 Maths Chapter 2 Polynomials graphical representation of polynomials – Part 12
- Class 10 Maths Chapter 2 Polynomials (Cubic Polynomials ) – Part 11
- Class 10 Maths Chapter 2 Polynomials zeroes of polynomials – Part 10
- Class 10 Maths Chapter 2 Polynomials formation – Part 9
- Class 10 Maths Chapter 2 Forming Quadratic Polynomials – Part 8
- Class10 Maths Chapter2 Polynomials MCQ – Part 7
- Class10 Maths Chapter2 Polynomials, missing coefficients – Part 6
- Class 10 Maths Chapter 2 Polynomials MCQ – Part 5
- Class10 Maths Chapter2 Polynomials (Zeroes of Polynomial) – Part 4
- Class 10 Social Science: Project Tiger, Green Revolution
Latest Posts
- Who was Isaac Newton? – Life, Discoveries, Laws of Motion & Gravity
- Class 9 Maths Chapter 3 Coordinate Geometry
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
- Class 7 Maths Chapter 2 Fractions and Decimals
- Class 8 Maths Chapter 3 Understanding Quadrilaterals
Join Our Other Communities
Instagram , Youtube , Facebook
