Here are some multiple-choice questions (MCQs) for Chapter 3 of Class 10 Maths (Pair of Linear Equations in Two Variables). You can find them online along with the answers. These questions are designed to help students do well in their board exams. They’re based on the latest CBSE syllabus (2024-2025) and NCERT textbook. Our experts have prepared these MCQs according to the current exam pattern. Practicing them will improve your problem-solving skills. You can click the link to access MCQs for each chapter and download a PDF for extra practice questions.
Class 10 Maths MCQs for Pair of Linear Equations in Two Variables
Question: In a pair of linear equations, how many variables are involved?
a) One
b) Two
c) Three
d) None of the above
Answer: b) Two
Question: Which of the following is a pair of linear equations in two variables?
a) x = 2
y = 3
b) 2x + 3y = 5
3x – 2y = 7
c) x^2 + y^2 = 25
x + y = 10
d) 3x + 2y = 4
2x + y = 5
Answer: b) 2x + 3y = 5, 3x – 2y = 7
Question: What is the general form of a linear equation in two variables?
a) ax^2 + by^2 = c
b) ax + by = c
c) ax^2 + by = c
d) ax + by^2 = c
Answer: b) ax + by = c
Question: Which method is used to solve a pair of linear equations graphically?
a) Substitution method
b) Elimination method
c) Cross-multiplication method
d) Graphical method
Answer: d) Graphical method
Question: If the pair of equations has a unique solution, what does it represent geometrically?
a) Parallel lines
b) Coincident lines
c) Intersecting lines
d) No solution
Answer: c) Intersecting lines
Question: How many solutions does a consistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: a) One
Question: If the pair of equations has no solution, what does it represent geometrically?
a) Parallel lines
b) Coincident lines
c) Intersecting lines
d) No solution
Answer: a) Parallel lines
Question: What does the elimination method involve in solving a pair of linear equations?
a) Adding or subtracting the equations to eliminate one variable
b) Substituting one equation into another to find the solution
c) Graphing the equations to find their intersection
d) Solving each equation separately and then comparing the solutions
Answer: a) Adding or subtracting the equations to eliminate one variable
Question: Which method involves expressing one variable in terms of the other and substituting it into the second equation?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: b) Substitution method
Question: What is the solution of the system of equations: 2x – 3y = 5, x + y = 3?
a) x = 2, y = 1
b) x = 1, y = 2
c) x = 3, y = 0
d) x = 0, y = 3
Answer: a) x = 2, y = 1
Question: If the lines represented by the equations are coincident, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: c) Infinite
Question: What is the solution of the system of equations: 3x – 2y = 4, 2x + y = 1?
a) x = 1, y = 2
b) x = 2, y = 1
c) x = 3, y = 4
d) x = 4, y = 3
Answer: a) x = 1, y = 2
Question: If the lines represented by the equations are parallel, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: d) None
Question: Which of the following is an inconsistent pair of linear equations?
a) 3x + 2y = 6, 6x + 4y = 10
b) 2x – y = 3, 4x – 2y = 6
c) 3x + 4y = 8, 6x + 8y = 16
d) 2x + y = 5, 4x + 2y = 10
Answer: d) 2x + y = 5, 4x + 2y = 10
Question: What is the solution of the system of equations: x – y = 2, 3x + y = 6?
a) x = 1, y = -1
b) x = 2, y = 0
c) x = 3, y = 1
d) x = 4, y = 2
Answer: b) x = 2, y = 0
Question: How many solutions does an inconsistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: d) None
Question: What is the solution of the system of equations: 5x + 3y = 7, 10x + 6y = 14?
a) x = 1, y = 1
b) x = 2, y = 1
c) x = 3, y = 2
d) x = 4, y = 3
Answer: a) x = 1, y = 1
Question: Which method involves solving one equation for one variable and then substituting it into the other equation?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: b) Substitution method
Question: What is the solution of the system of equations: 2x – 5y = 3, 4x – 10y = 6?
a) x = 1, y = -1
b) x = 2, y = 1
c) x = 3, y = 2
d) x = 4, y = 3
Answer: a) x = 1, y = -1
Question: What is the solution of the system of equations: 3x + 4y = 10, 6x + 8y = 14
a) x = 1, y = 1
b) x = 2, y = 1
c) x = 3, y = 2
d) x = 4, y = 3
Answer: b) x = 2, y = 1
Question: What is the solution of the system of equations: 2x + 3y = 8, 4x + 6y = 16?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: Which method involves adding or subtracting the equations to eliminate one variable?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: c) Elimination method
Question: What is the solution of the system of equations: 3x – 4y = 10, 6x – 8y = 20?
a) x = 2, y = -1
b) x = 3, y = -2
c) x = 4, y = -3
d) x = 5, y = -4
Answer: a) x = 2, y = -1
Question: If the lines represented by the equations are coincident, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: c) Infinite
Question: What is the solution of the system of equations: 2x – 3y = 6, 4x – 6y = 12?
a) x = 2, y = -1
b) x = 3, y = -2
c) x = 4, y = -3
d) x = 5, y = -4
Answer: d) x = 5, y = -4
Question: If the lines represented by the equations are parallel, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: d) None
Question: What is the solution of the system of equations: 5x – 2y = 8, 10x – 4y = 16?
a) x = 2, y = 2
b) x = 3, y = 3
c) x = 4, y = 4
d) x = 5, y = 5
Answer: a) x = 2, y = 2
Question: How many solutions does a consistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: a) One
Question: What is the solution of the system of equations: 3x + 2y = 9, 6x + 4y = 18?
a) x = 1, y = 1
b) x = 2, y = 2
c) x = 3, y = 3
d) x = 4, y = 4
Answer: b) x = 2, y = 2
Question: If the lines represented by the equations are coincident, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: c) Infinite
Question: What is the solution of the system of equations: 2x + 4y = 12, 4x + 8y = 24?
a) x = 1, y = 2
b) x = 2, y = 4
c) x = 3, y = 6
d) x = 4, y = 8
Answer: a) x = 1, y = 2
Question: Which method involves solving one equation for one variable and then substituting it into the other equation?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: b) Substitution method
Question: What is the solution of the system of equations: 3x + 2y = 7, 6x + 4y = 14?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: What is the solution of the system of equations: 4x + 3y = 14, 8x + 6y = 28?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: How many solutions does an inconsistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: d) None
Question: What is the solution of the system of equations: 3x – 2y = 8, 6x – 4y = 16?
a) x = 2, y = -2
b) x = 3, y = -3
c) x = 4,
Answer: a) x = 2, y = -2
Question: Which method involves adding or subtracting the equations to eliminate one variable?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: c) Elimination method
Question: What is the solution of the system of equations: 5x – 3y = 7, 10x – 6y = 14?
a) x = 1, y = 1
b) x = 2, y = 2
c) x = 3, y = 3
d) x = 4, y = 4
Answer: a) x = 1, y = 1
Question: What is the solution of the system of equations: 2x + 5y = 13, 4x + 10y = 26?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: How many solutions does a consistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: a) One
Question: What is the solution of the system of equations: 3x + 2y = 9, 6x + 4y = 18?
a) x = 1, y = 1
b) x = 2, y = 2
c) x = 3, y = 3
d) x = 4, y = 4
Answer: b) x = 2, y = 2
Question: If the lines represented by the equations are coincident, how many solutions does the system have?
a) One
b) Two
c) Infinite
d) None
Answer: c) Infinite
Question: What is the solution of the system of equations: 2x + 4y = 12, 4x + 8y = 24?
a) x = 1, y = 2
b) x = 2, y = 4
c) x = 3, y = 6
d) x = 4, y = 8
Answer: a) x = 1, y = 2
Question: Which method involves solving one equation for one variable and then substituting it into the other equation?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: b) Substitution method
Question: What is the solution of the system of equations: 3x + 2y = 7, 6x + 4y = 14?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: What is the solution of the system of equations: 4x + 3y = 14, 8x + 6y = 28?
a) x = 1, y = 2
b) x = 2, y = 3
c) x = 3, y = 4
d) x = 4, y = 5
Answer: a) x = 1, y = 2
Question: many solutions does an inconsistent pair of linear equations have?
a) One
b) Two
c) Infinite
d) None
Answer: d) None
Question: What is the solution of the system of equations: 3x – 2y = 8, 6x – 4y = 16?
a) x = 2, y = -2
b) x = 3, y = -3
c) x = 4, y = -4
d) x = 5, y = -5
Answer: a) x = 2, y = -2
Question: Which method involves adding or subtracting the equations to eliminate one variable?
a) Graphical method
b) Substitution method
c) Elimination method
d) Matrix method
Answer: c) Elimination method
Question: What is the solution of the system of equations: 5x – 3y = 7, 10x – 6y = 14?
a) x = 1, y = 1
b) x = 2, y = 2
c) x = 3, y = 3
d) x = 4, y = 4
Answer: a) x = 1, y = 1
