Solve Linear Equations Like a Pro with Our MCQ Mock Test!

Are you confident in solving pairs of linear equations in two variables? Test your skills and sharpen your problem-solving techniques with our Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables MCQ Mock Test!

This test is designed to help you master methods like substitution, elimination, and cross-multiplication, while also understanding graphical solutions. Each question challenges your logical reasoning and calculation skills, just like in your board exams.

What You’ll Get:

  • A variety of MCQs covering all important methods of solving linear equations.
  • Detailed explanations to clear every doubt.
  • Instant results to evaluate your preparation and identify weak areas.
  • Practice that builds speed, accuracy, and confidence.

Why Attempt This Test?
Because solving linear equations is not just about numbers — it’s about thinking logically. This mock test ensures you’re ready to tackle any question with ease.

Take the test now and master pairs of linear equations in two variables!

1. Match the Column:

(1) 2x + 3y = 40
6x + 5y = 10		 (A) Coincident lines
(2) 2x + 3y = 40
6x + 9y = 50		 (B) Intersecting lines
(3) 2x + 3y = 10
4x + 6y = 20		 (C) Parallel lines
 
 
 
 

2. The value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is

 
 
 
 

3. The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if

 
 
 
 

4. On solving the following pair of linear equations: 2x – y = 2; 5x + 2y = 14 by substitution method, values of x and y are _______ and _______ respectively.

 
 
 
 

5. The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference between the two digits of the number?

 
 
 
 

6. If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then the respective values of a and b are

 
 
 
 

7. The father’s age is six times of his son’s age. Four years hence, the age of the father will be four times of his son’s age. The present ages, in years, of the son and the father are, respectively.

 
 
 
 

8. If a pair of linear equations in two variables is consistent, then the linens represented by two equations are:

 
 
 
 

9. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): x = 2, y = 1 is a solution of pair of equations 3x – 2y = 4 and 2x + y = 5.
Reason (R): A pair of values (x, y) satisfying each one of the equations in a given system of two simultaneous linear equations in x and y is called a solution of the system of equations.

 
 
 
 

10. A pair of linear equations which has a unique solution x = 2, y = –3 is

 
 
 
 

11. The pair of equations y = 0 and y = –7 has

 
 
 
 

12. Using the following equations:   + 6y = 10;   – 6y = 5, find the value of p if p = 5x.

 
 
 
 

13. Match the Column:

(1) 2x + 5y = 10
3x + 4y = 7		 (A) Unique solution
(2) 2x + 5y = 10
6x + 15y = 20		 (B) Infinitely many
solutions
(3) 5x + 2y = 10
10x + 4y = 20		 (C) No common solution
 
 
 
 

14. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): The system of equations x + 2y – 5 = 0 and 2x – 6y + 9 = 0 has infinitely many solutions.
Reason (R): The system of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 has infinitely many solutions when

 
 
 
 

15. The equations ax + by + c = 0 and dx + ey + c = 0 represent the same straight line if

 
 
 
 

16. a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where a1, b1, c1, a2, b2, c2 are all real numbers and a12 + b12 ≠ 0, a22 + b22 ≠ 0, is called a

 
 
 
 

17. The pair of equations x = a and y = b graphically represents lines which are

 
 
 
 

Question 1 of 17