CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02

Find CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 right below. We offer free printable Class 10 Mathematics worksheets in PDF for Chapter 3 Pair of Linear Equations in Two Variables. Built by expert teachers for the 2026-27 session, these practice exercises align with standard CBSE, NCERT, and KVS patterns.

Chapter 3 Pair of Linear Equations in Two Variables Mathematics Practice Worksheet for Class 10

Every student of Class 10 Mathematics should practice with these chapter-wise worksheets. They provide great questions and solutions for Chapter 3 Pair of Linear Equations in Two Variables to boost your confidence. Practicing these Class 10 Mathematics sheets regularly makes you faster and more accurate for your 2026-27 exams.

Download Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Worksheet PDF

Linear Equations in Two Variables

  • Linear Equations

  • Solution of a Linear Equation

  • Graph of a Linear Equation in Two Variables
  • Equations of Lines Parallel to x-axis and y-axis

 

  • An equation of the form \( ax + by + c = 0 \) where \( a \), \( b \) and \( c \) are real numbers such that \( a \) and \( b \) are not both zero is called a linear equation in two variables.
  • A pair of values of \( x \) and \( y \) which satisfy the equation \( ax + by + c = 0 \) is called a solution of the equation.
  • Graph: The graph of every linear equation in two variables is a straight line. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Conversely, every solution of the linear equation is a point on the graph of the linear equation.
  • A linear equation in two variables has infinitely many solutions.
  • The graph of every linear equation in two variables is a straight line.
  • \( y = 0 \) is the equation of x-axis and \( x = 0 \) is equation of y-axis.
  • The graph of \( x = a \) is a straight line parallel to the y-axis.
  • The graph of \( y = a \) is a straight line parallel to the x-axis.
  • An equation of the type \( y = mx \) represent a line passing through the origin.


Multiple Choice Questions (MCQs)

Choose the correct answer from the given options:

Question. The pair of linear equations 3x/2 + 5y/3 = 7 and 9x + 10y = 14 is
(a) consistent
(b) inconsistent
(c) consistent with one solution
(d) consistent with many solutions
Answer : B

Question. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
(a) −14/3
(b) 2/5
(c) 5
(d) 10
Answer : D

Question. If a pair of linear equations is consistent, then the line represented by them are
(a) parallel
(b) intersecting or coincident
(c) always coincident
(d) always intersecting
Answer : B

Question. The value of k for which the system of equations kx + 4y = k – 4, 16x + ky = k have infinite number of solutions is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8
Answer : D

Question. The value of k for which the system of linear equations 3x + y = 1, (2k –1)x + (k –1)y = 2k + 1 have no solution is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8
Answer : A

Question. If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is
(a) Only 4
(b) Only 5
(c) Only 6
(d) Any number other than –6
Answer : D

Question. The value of k for which the given system has unique solution 2x + 3y – 5 = 0, kx – 6y – 8 = 0 is
(a) k = 2
(b) k ≠ 4
(c) k = 4
(d) k ≠ 4
Answer : D

Question. For what value of k, the following system of equations have infinite solutions: [Imp.]
2x – 3y = 7, (k + 2)x – (2k + 1)y = 3 (2k – 1)?
(a) k = 2
(b) k = 3
(c) k = 4
(d) k = 8
Answer : C

Question. The value of m for which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions is
(a) 5
(b) 8
(c) – 5
(d) 8
Answer : A

v For what values of p, the pair of equations 4x + py +8 =0 and 2x +2y +2 = 0 have unique solution?
(a) p = 4
(b) p ≠ 4
(c) p = 7
(d) p ≠ 7
Answer : B

vWhat type of straight lines will be represented by the system of equations 2x + 3y = 5 and 4x + 6y = 7?
(a) Intersecting
(b) Parallel
(c) Conincident
(d) None of these
Answer : B

Question. For what value of p, the following pair of linear equations have infinitely many solutions?
(p – 3)x + 3y = p, px + py = 12
(a) 4
(b) 6
(c) 9
(d) 11
Answer : B

Question. The value of k for which the following pair of linear equations have infinitely many solutions:
2x + 3y = 7, (k – 1)x + (k + 2)y = 3k is
(a) 2
(b) 4
(c) 7
(d) 9
Answer : C

Question. The value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : A
 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of
assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Pair of linear equations x + y = 14, x – y = 4 is consistent.
Reason (R): By comparing a1/a2 and b1/b2 if we get a1/a2 ≠ b1/b2, then given system of equations is consistent.
Answer : A

Question. Assertion (A): For k = 6, the system of linear equations x + 2y + 3 = 0 and 3x + ky + 6 = 0 is inconsistent.
Reason (R): The system of linear equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 is inconsistent if a1/a2 = b1/b2 = c1/c2
Answer : C

 

PAIRS OF LINEAR EQUATIONS IN TWO VARIABLES

Q.- Solve the following system of equations.
x – z = 5
y + z = 3
x – y = 2
 
Answer : The given system of equations to ;
x – z = 5                  ....(1)
y + z = 3                 ....(2)
x – y = 2                .....(3)
From equation (1), we have;
z = x – 5
Putting z = x – 5 in equation (2), we get ;
y + x – 5 = 3
=> x + y = 8     ....(4)
Adding equations (3) and (4), we get;
2x = 10
=>x = 5
Again putting x = 5 in equation (1), we get;
5 – z = 5
=>z = 0
Hence, the solution of the given system of
equation is x = 5, y = 3, z = 0.
 
Other method :
adding (1), (2) & (3)
2x = 10
x = 5
now put this value in equation (1) & (3), we get z = 0, y = 3 respectively
 
Q.- Solve,
x + 2y + z = 12
2x – z = 4
x – 2y = 4
Answer : We have,
x + 2y + z = 12     ....(1)
2x – z = 4             ....(2)
x – 2y = 4             ....(3)
From equation (1), we have z = 12 – x – 2y.
Putting, z = 12 – x – 2y in the equation (2), we get;
2x – (12 – x – 2y) = 4
=> 2x – 12 + x + 2y = 4
=> 3x + 2y = 16      ....(4)
Adding equations (3) and (4), we get;
4x = 20
=> x = 5
Putting the value of x = 5 in equation (2), we get
2 × 5 – z = 4
=> z = 10 – 4 = 6
Again putting the value of x = 5 in equation (3), we get
5 – 2y = 4 => y = 1/2
Hence, the solution of the given system of equations is ;
x = 5, y = 1/2 , z = 6
 
 
Section A
 
1. Find the value of k for which the pair of linear equations 4x + 6y – 1 = 0 and 2x + ky - 7 =0 represent parallel lines.
Answer : k = 3)
 
2. If x = a and y = b is the solution of equations x – y = 2 and x + y = 4, find a and b .
Answer : a = 3, b =1)
 
3. The pair of equations y =0 and y = -7 has how many solutions?
Answer : no solution)
 
4. If one equation of a pair of dependent linear equations is - 5x + 7y = 2, give a possible second equation.
5. Find k if the pair of linear equations kx + 2y = 5 and 3x+ y = 1 has unique solutions.
Answer : k is any real number except 6)
 
6. The pair of linear equations 4x + 6y = 12 and 2x +3y =6 has how many solutions?
Answer : Infinitely many solutions)
 
7. What does each solution (x, y) of a linear equation in two variables ax + by + c =0 (a≠0, b≠0) correspond to?
 
Answer : A point on the line representing the given equation)
 
8. Give the condition that the system of equations a1 x+ b1 y = c1 and a 2 x+ b 2 y = c 2 has unique solution.
Answer : a1 / a 2 ≠ b1 /b 2)
 
9. Find the area of the triangle formed by the coordinate axes and line x + y = 6 is :
Answer : 18 sq units )
 
10. The equation 2x – y = 12 and the equation 3ax + 2by = 18 represents two parallel lines. Find the value of a:b
(Answer : 4:3) 
 
Section B
 
11. For which value of p does the pair of equations given below has unique solution? 4x + py+ 8 = 0 and 2x + 2y + 2 = 0.
Answer : p is any real no.except 4)
 
12. For what value of k1 the following system of linear equations have no solution: 3x + y =1 and (2k-1)x + (k-1)y = 2k + 1
Answer :  k = 2
 
13. Solve for x and y: 37x + 43y =123 ; 43x + 37y = 117
 
Answer : x=1; y = 2)
 
14. Solve for x and y: 4x +6/y =15 and 3x - 4/y  = 7
 
vx = 3, y = 2)
 
15. For what value of k, 2x + 3y = 4 and (k + 2) x + 6y = 3k + 2 will have infinitely many solutions?
 
(Answer : k = 2)
 
16. For what value of k the following equations have unique solution 2x + ky = 1 and 3x – 5y = 7?
 
Answer : k is any real number except -10/3)
 
17. Determine a and b for which the system of linear equation has infinite number of solutions.
 
(2a -1) x + 3y -5 = 0 and 3x + (b -1)y – 2 =0
 
Answer :  a = 17/4  b = 11/5)
 
18. For what value of p will the following system of equations have no solution
 
(2p – 1)x + (p -1) y = 2p + 1 and y + 3x – 1 = 0
 
Answer : p = 2
 
19. Is the system of linear equations 2x + 3y = 9 and 4x + 6y = 18, consistent?
 
Answer : consistent and dependent)
 
20. Without drawing the graph, find out whether the line representing by the following pair of equations, intersect at a point ,are parallel or are coincident.
9x – 10y = 21 and 3/2 x - 5/3 y =7/2
 
Answer : co-incident
 
Section C
 
21. Solve the following equations graphically:
 
(i) 3x + y + 4 = 0          (ii) 3x- 4y -12 = 0      (iii) x + y =3
    6x - 2y + 4= 0                x +2y – 4= 0             3x+ 3y=9
 
(iv) 2x+ 7y =11
      5x + 35/2y =25  
 
Answer : (i) x= -1,y= -1   (iii) infinite solutions   (ii) x= 4, y= 0   (iv) no solution)
 
22. For what values of a and b does the following pair of linear equations have infinite number of solutions?2x + 3y= 7, a (x+y) – b (x-y) =3a + b - 2 ( Ans 5; 1)
 
23. In a bag containing red and white balls, half the number of white balls is equal to one-third the number of red balls. Thrice the total number of balls exceeds seven times the number of white balls by 6. How many balls of each colour does the bag contain?
 
Answer : 18;12)
 
24. Solve the following pair of linear equations by substitution method:
3x + 2y -7=0
4x + y - 6=0
Answer : x=1; y=2)
 
25. Solve using cross multiplication method :
5x + 4y – 4=0
x – 12y – 20=0
Answer : x=2; y =- 3/2)
26. Solve the following equations:
 
a) 8x – 9y = 6xy ; 10x+6y=19xy
Answer : x=0;y=0 or x=2/3 y= 3/2 )
b) 6(ax + by) = 3a + 2b ; 6(bx + ay) = 3b – 2a
Vx = 1/2 ; y = 1/3 )
 
27. The difference between two numbers is 26 and one number is three times the other. Find the numbers.
Answer : 39; 13)
 
28. A fraction becomes 9/11 if 2 added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 5/6 . Find the fraction.
Answer : 7/9
 
29. A two digit number is obtained either by multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of digits by 16 and adding 3. Find the number.
Answer : 83
 
30. The age of the father is twice the sum of the ages of his 2 children. After 20 years his age will be equal to the sum of the ages of his children. Find the age of the father.
Answer : 40 yrs
 
Section D 
 
31. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and
 
32. A and B are two points 150 km apart on a highway. Two cars start from A and B at the same time. If they move in the same direction they meet in 15 hours. But if they move in the opposite direction, they meet in 1 hour. Find their speeds.
Answer : 80km/hr ; 70km/hr
 
33. Draw the graphs of the pair of linear equations:
x+ 2y = 5 and 2x – 3y = -4
Also find the points where the lines meet the x-axis.
Answer : (5,0) ,(-2,0)
 
34. Solve the following pair of linear equations graphically:
2x + 3y = 12 and x – y = 1.
Find the area of the region bounded by the two lines representing the above equations and y-axis.
Answer : 7.5 sq units)
 
35. Solve the following pair of linear equations graphically:
x+ 3y = 6 , 2x – 3y = 12
Also shade the region bounded by the line 2x - 3y = 12 and both the co-ordinate axes.
Vx = 6, y = 0)
 
36. Raghav scored 70 marks in a test, getting 4 marks for each right answer and losing 1 mark for each wrong answer. Had 5 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, then Raghav would have scored 80 marks. How many questions were there in the test? Which values would have Raghav violated if he resorted to unfair means?
Answer : 30 ; honesty)
 
37. The incomes of two persons A and B are in the ratio 8:7 and the ratio of their expenditures is 19:16 . If their savings are Rs2550 per month, find their monthly income. What is the importance of saving in life?
Answer : Rs 12240,Rs 10710 ; value)
 
38. Three lines x + 3y = 6, 2x - 3y= 12 and x = 0 are enclosing a beautiful triangular park. Find the points of intersection of the lines graphically and the area of the park, if all measurements are in km. What type of behaviour should be expected by public in these types of parks?
Answer : 18 km 2 ; value)
 
39 A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Shristi paid Rs27 for a book kept for seven days, while Rekha paid Rs 21 for the book she kept for five days. Find the fixed charge and the additional charge paid by them. What is the importance of library?
Answer : Rs15, Rs 12, Rs 6; importance)
 
40. In a painting competition of a school a child made Indian national flag whose perimeter was 50 cm. Its area will be decreased by 6 square cm, if length is decreased by 3 cm and breadth is increased by 2cm,then find the dimensions of the flag? What does the saffron colour in the flag signify?
Answer : 15cm; 10cm; courage and sacrifice)
 
 

Please click on below link to download CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set B

Free study material for Mathematics

Exam Preparation Worksheet for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables

Download Practice Sheet: Chapter 3 Pair of Linear Equations in Two Variables (Class 10 Mathematics)

Review the Chapter 3 Pair of Linear Equations in Two Variables practice sheet above to stay ahead in your school evaluations. Designed to meet the newest CBSE standards for Class 10 Mathematics, these printable problem sets are available as a convenient PDF format download. Regular practice on frequently tested topics guarantees stronger exam performance.

Expert NCERT Practice Material for Class 10 Mathematics

Compiled using the standard NCERT book for Class 10 Mathematics, these practice exercises ensure accurate guidance. Completing the questions should be followed by checking our comprehensive NCERT solutions, designed to teach clear techniques for Mathematics questions. Every resource is available free of cost.

More Practice Materials for CBSE Examinations

Maximize your performance in Class 10 by taking the interactive Mathematics MCQ test for this topic. Explore our website for additional printable assignments tailored for Class 10 Mathematics. Routine practice drives test confidence and maximizes success in CBSE board exams.

FAQs

Where can I download the latest PDF for CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02?

You can download the teacher-verified PDF for CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 from StudiesToday.com. These practice sheets for Class 10 Mathematics are designed as per the latest CBSE academic session.

Are these Mathematics Class 10 worksheets based on the 2026-27 competency-based pattern?

Yes, our CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 includes a variety of questions like Case-based studies, Assertion-Reasoning, and MCQs as per the 50% competency-based weightage in the latest curriculum for Class 10.

Do you provide solved answers for CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02?

Yes, we have provided detailed solutions for CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 to help Class 10 and follow the official CBSE marking scheme.

How does solving CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 help in exam preparation?

Daily practice with these Mathematics worksheets helps in identifying understanding gaps. It also improves question solving speed and ensures that Class 10 students get more marks in CBSE exams.

Is there any charge for the Class 10 Mathematics practice test papers?

All our Class 10 Mathematics practice test papers and worksheets are available for free download in mobile-friendly PDF format. You can access CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set 02 without any registration.