Pair of Linear Equations in Two Variables helps students understand how two equations can be solved together to find unknown values. The chapter covers algebraic methods, graphical representation, and real-life applications involving prices, speeds, and other mathematical situations. Practicing Pair of Linear Equations in Two Variables MCQs helps students improve equation-solving skills, logical reasoning, and accuracy for Class 10 Maths exams.
Developing a clear understanding of these concepts makes it easier to solve application-based problems and interpret graphical solutions. Students can practice chapter-wise MCQs and explore Class 10 MCQs to strengthen their preparation. Additional CBSE Board resources can help students revise important concepts and prepare for objective questions based on the latest syllabus.
What Students Learn in Pair of Linear Equations Class 10
This chapter is not only about solving equations. It mainly focuses on understanding how two algebraic relationships interact mathematically.
Students learn:
- How two variables are connected
- How graphs represent equations visually
- Why some equations have one solution while others have none
- How algebra helps solve practical situations
- Different mathematical approaches for finding unknown values
The chapter also improves analytical problem-solving, which becomes useful in higher mathematics later.
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Class 10 Maths Chapter 3 MCQs with Answers and Explanations
Make your daily Maths practice more useful by solving these Class 10 Pair of Linear Equations in Two Variables MCQs. These objective questions help students strengthen conceptual understanding, improve calculation accuracy, and develop faster equation-solving skills for board exams.
Q1. The pair of equations 2x + 4y - 8 = 0 and x + 2y - 4 = 0 has:
A) One solution
B) No solution
C) Infinitely many solutions
D) Exactly two solutions
Answer: C
Explanation: Both equations represent the same straight line because all coefficients are proportional. Therefore, the system has infinitely many solutions.
Q2. If two linear equations intersect at one point, then the system is called:
A) Inconsistent
B) Dependent
C) Consistent with unique solution
D) Parallel system
Answer: C
Explanation: Intersecting lines always meet at one point, so the equations have exactly one common solution.
Q3. The equations 5x + 2y = 7 and 10x + 4y = 9 represent:
A) Coincident lines
B) Parallel lines
C) Intersecting lines
D) Perpendicular lines
Answer: B
Explanation: The ratios of coefficients of x and y are equal, but the constants are different. Hence, the lines are parallel.
Q4. If the equations 4x + ky = 12 and 8x + 2y = 6 are parallel, the value of k is:
A) 1
B) 2
C) 4
D) 8
Answer: B
Explanation: For parallel lines, the ratios of coefficients of x and y must be equal. Solving 4/8 = k/2 gives k = 2.
Q5. Which pair of equations represents coincident lines?
A) x + y = 5 and 2x + 2y = 10
B) x - y = 3 and x - y = 5
C) 3x + y = 7 and x + y = 7
D) 2x - y = 4 and x + y = 9
Answer: A
Explanation: The second equation is exactly twice the first equation, so both equations represent the same line.
Q6. Solve: x + y = 9 and x - y = 3
A) x = 5, y = 4
B) x = 6, y = 3
C) x = 7, y = 2
D) x = 4, y = 5
Answer: B
Explanation: Adding the equations gives 2x = 12, so x = 6. Substituting into x + y = 9 gives y = 3.
Q7. A fraction becomes 1/2 when 2 is added to the numerator and 1/3 when 3 is added to the denominator. The fraction is:
A) 3/6
B) 4/9
C) 5/12
D) 6/11
Answer: B
Explanation: Let the fraction be x/y. Forming and solving the equations gives x = 4 and y = 9.
Q8. The equations 6/x + 2y = 10 and 3/x - y = 1 give the value of x as:
A) 1/2
B) 2
C) 3
D) 1/3
Answer: A
Explanation: Let 1/x = m. Solving the equations gives m = 2, so x = 1/2.
Q9. The pair of equations 4x - y = 3 and 8x - 2y = 8 graphically represent:
A) Intersecting lines
B) Parallel lines
C) Coincident lines
D) Vertical lines
Answer: B
Explanation: The ratios of x and y coefficients are equal, but the constant ratios are unequal. Hence, the lines are parallel.
Q10. The equations y = 5 and y = -3 represent:
A) Coincident lines
B) Intersecting lines
C) Parallel horizontal lines
D) Perpendicular lines
Answer: C
Explanation: Both equations represent horizontal lines with different intercepts, so they never meet.
Q11. The lines x = 2 and y = -1 intersect at:
A) (2, -1)
B) (-1, 2)
C) (1, 2)
D) (-2, 1)
Answer: A
Explanation: x = 2 is a vertical line and y = -1 is a horizontal line. They intersect at (2, -1).
Q12. The graph of x = 7 is always:
A) Parallel to x-axis
B) Parallel to y-axis
C) Passing through origin
D) Slanting line
Answer: B
Explanation: Any equation of the form x = constant represents a vertical line parallel to the y-axis.
Q13. If y = 4 in the equation 2x + y = 14, then x equals:
A) 3
B) 4
C) 5
D) 6
Answer: C
Explanation: Substituting y = 4 gives 2x + 4 = 14. Therefore, x = 5.
Q14. The equations 2x + 3y = 6 and 4x + 6y = 12 have:
A) One solution
B) No solution
C) Infinite solutions
D) Two solutions
Answer: C
Explanation: The second equation is obtained by multiplying the first equation by 2, so the lines coincide.
Q15. Two numbers are in the ratio 3:5. If 4 is added to each number, the ratio becomes 5:7. The numbers are:
A) 6 and 10
B) 9 and 15
C) 12 and 20
D) 15 and 25
Answer: B
Explanation: Let the numbers be 3x and 5x. Solving the ratio equation gives x = 3.
Q16. The solution of x + y = 11 and x - y = 1 is:
A) x = 5, y = 6
B) x = 6, y = 5
C) x = 4, y = 7
D) x = 7, y = 4
Answer: B
Explanation: Adding the equations gives 2x = 12, so x = 6. Substituting gives y = 5.
Q17. A mother is four times as old as her daughter. After 8 years, the mother will be twice the daughter's age. Their present ages are:
A) 8 and 32
B) 10 and 40
C) 12 and 48
D) 6 and 24
Answer: A
Explanation: Let daughter's age be x and mother's age be 4x. Solving gives x = 8 and mother’s age = 32.
Q18. The equations x = 5 and y = 3 intersect at:
A) (3, 5)
B) (5, 3)
C) (-5, 3)
D) (5, -3)
Answer: B
Explanation: The vertical line x = 5 and horizontal line y = 3 meet at (5, 3).
Q19. The value of k for which the equations x + 2y = 5 and 2x + ky = 10 have infinitely many solutions is:
A) 2
B) 4
C) 5
D) 10
Answer: B
Explanation: For infinitely many solutions, the ratios of all coefficients must be equal. Solving gives k = 4.
Q20. The equations y = 2 and y = 8 are:
A) Intersecting lines
B) Coincident lines
C) Parallel lines
D) Perpendicular lines
Answer: C
Explanation: Both are horizontal lines with different intercepts, so they are parallel.
Q21. If the equations 5x + ky = 10 and 10x + 4y = 12 are parallel, k equals:
A) 1
B) 2
C) 4
D) 5
Answer: B
Explanation: For parallel lines, 5/10 = k/4. Solving gives k = 2.
Q22. A linear equation in two variables always forms a:
A) Circle
B) Straight line
C) Curve
D) Triangle
Answer: B
Explanation: Linear equations represent straight lines on a coordinate plane.
Q23. The equations 3x - 2y = 9 and 6x - 4y = 18 have:
A) One solution
B) No solution
C) Infinite solutions
D) Two solutions
Answer: C
Explanation: The second equation is double the first equation, so both lines coincide.
Q24. Two straight lines are parallel when:
A) Their slopes are equal
B) Their slopes are negative
C) Their intercepts are same
D) They cross each other
Answer: A
Explanation: Parallel lines have equal slopes and never intersect.
Q25. The equations x + 3y = 7 and 2x + 6y = 14 have:
A) One solution
B) Infinite solutions
C) No solution
D) Exactly two solutions
Answer: B
Explanation: The second equation is twice the first equation, so both represent the same line.
Q26. If the equations kx + y = 6 and 2x + 2y = 5 have no solution, then k equals:
A) 1
B) 2
C) 3
D) 4
Answer: A
Explanation: For no solution, the coefficient ratios of x and y must be equal while constants differ. Hence, k/2 = 1/2, so k = 1.
Q27. Reversing the digits of the number 72 gives:
A) 25
B) 27
C) 62
D) 37
Answer: B
Explanation: Reversing the positions of 7 and 2 forms the number 27.
Q28. The equations 4x - y = 8 and kx - 2y = 5 have a unique solution when:
A) k = 8
B) k = 4
C) k ≠ 8
D) k ≠ 4
Answer: C
Explanation: A unique solution exists when coefficient ratios are unequal. Therefore, k should not make the ratios equal.
Q29. The value of p if the point (3, p) lies on the line x + 2y = 11 is:
A) 2
B) 3
C) 4
D) 5
Answer: C
Explanation: Substituting x = 3 gives 3 + 2p = 11. Solving gives p = 4.
Q30. The equations ax + y = 4 and 2x + by = 8 represent parallel lines if:
A) ab = 2
B) ab = 4
C) ab = 6
D) ab = 8
Answer: A
Explanation: For parallel lines, a/2 = 1/b. Cross-multiplying gives ab = 2.
Important Areas Covered in Pair of Linear Equations in Two Variables
Most Pair of Linear Equations Class 10 MCQs with Answers are created from these important concepts:
Equation Fundamentals
- Linear equations in two variables
- Standard equation form
- Meaning of coefficients and variables
Graph-Based Concepts
- Graphical representation of equations
- Intersecting lines
- Parallel lines
- Coincident lines
Algebraic Solving Methods
- Substitution method
- Elimination method
- Cross multiplication method
Application-Based Topics
- Word problems
- Cost comparison questions
- Age-based equations
- Distance and speed problems
Why This Chapter is Important for CBSE Board Exams
This chapter has strong weightage because it tests multiple skills simultaneously. Board exam questions often check :
- conceptual clarity,
- graph interpretation,
- equation formation,
- logical elimination,
- and application understanding.
Many students lose marks, not because the chapter is difficult, but because they rush calculations or misunderstand the relationship between equations. Questions from this chapter are frequently asked in :
- objective sections,
- case-study formats,
- assertion-reason questions,
- and competency-based assessments.
