CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set B

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Read and download free pdf of CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set B. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 3 Linear Equations Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

Chapter 3 Linear Equations Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

Class 10 Mathematics Chapter 3 Linear Equations Worksheet Pdf

 

PAIRS OF LINEAR EQUATIONS IN TWO VARIABLES

Q.- Solve the following system of equations.
x – z = 5
y + z = 3
x – y = 2
 
Sol. 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
 
Sol. 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.
 
(Ans: 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 .
 
(Ans: a = 3, b =1)
 
3. The pair of equations y =0 and y = -7 has how many solutions?
 
(Ans: 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.
 
(Ans: k is any real number except 6)
 
6. The pair of linear equations 4x + 6y = 12 and 2x +3y =6 has how many solutions?
 
(Ans: 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?
 
(Ans: 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.
 
(Ans: a1 / a 2 ≠ b1 /b 2)
 
9. Find the area of the triangle formed by the coordinate axes and line x + y = 6 is :
 
(Ans: 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
 
(Ans: -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.
 
(Ans: 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
 
(Ans: k = 2)
 
13. Solve for x and y: 37x + 43y =123 ; 43x + 37y = 117
 
(Ans: x=1; y = 2)
 
14. Solve for x and y: 4x +6/y =15 and 3x - 4/y  = 7
 
(Ans: x = 3, y = 2)
 
15. For what value of k, 2x + 3y = 4 and (k + 2) x + 6y = 3k + 2 will have infinitely many solutions?
 
(Ans: k = 2)
 
16. For what value of k the following equations have unique solution 2x + ky = 1 and 3x – 5y = 7?
 
(Ans: 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
 
(Ans: 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
 
(Ans: p = 2)
 
19. Is the system of linear equations 2x + 3y = 9 and 4x + 6y = 18, consistent?
 
(Ans: 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
 
(Ans: 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  
 
( Ans. (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?
 
(Ans 18;12)
 
24. Solve the following pair of linear equations by substitution method:
 
3x + 2y -7=0
4x + y - 6=0
 
(Ans x=1; y=2)
 
25. Solve using cross multiplication method :
 
5x + 4y – 4=0
x – 12y – 20=0
 
(Ans x=2; y =- 3/2)
 
26. Solve the following equations:
 
a) 8x – 9y = 6xy ; 10x+6y=19xy
 
(Ans x=0;y=0 or x=2/3 y= 3/2 )
 
b) 6(ax + by) = 3a + 2b ; 6(bx + ay) = 3b – 2a
 
(Ans x = 1/2 ; y = 1/3 )
 
27. The difference between two numbers is 26 and one number is three times the other. Find the numbers.
 
(Ans 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.
 
(Ans 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.
 
( Ans 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.
 
(Ans: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.
 
(Ans: 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.
 
(Ans : (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.
 
(Ans: 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.
 
(Ans x = 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?
 
(Ans : 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?
 
(Ans : 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?
 
(Ans: 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?
 
(Ans : 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?
 
(Ans : 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

Chapter 01 Real Numbers
CBSE Class 10 Mathematics Real Numbers And Polynomials Worksheet
CBSE Class 10 Mathematics Real Numbers Worksheet Set A
CBSE Class 10 Mathematics Real Numbers Worksheet Set B
CBSE Class 10 Mathematics Real Numbers Worksheet Set C
CBSE Class 10 Mathematics Real Numbers Worksheet Set D
CBSE Class 10 Mental Maths Real Numbers Worksheet
CBSE Class 10 Mental Maths Real Numbers Worksheet in Hindi
Chapter 02 Polynomials
CBSE Class 10 Mathematics Polynomials Worksheet Set A
CBSE Class 10 Mathematics Polynomials Worksheet Set B
CBSE Class 10 Mathematics Polynomials Worksheet Set C
CBSE Class 10 Mathematics Polynomials Worksheet Set D
CBSE Class 10 Mathematics Polynomials Worksheet Set E
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set B
CBSE Class 10 Mathematics Probability Worksheet Set A
CBSE Class 10 Mental Maths Polynomials Worksheet
CBSE Class 10 Mental Maths Polynomials Worksheet in Hindi
Chapter 03 Linear Equations
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set A
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set B
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set C
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set D
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set E
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set F
CBSE Class 10 Mathematics Pair of Linear Equation In Two Variables Worksheet Set G
CBSE Class 10 Mental Maths Pair Of Linear Equations In Two Variables Worksheet
CBSE Class 10 Mental Maths Pair Of Linear Equations In Two Variables Worksheet in Hindi
Chapter 04 Quadratic Equation
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set A
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set B
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set C
CBSE Class 10 Mathematics Quadratic Equations Worksheet Set D
CBSE Class 10 Mental Maths Quadratic Equations Worksheet
CBSE Class 10 Mental Maths Quadratic Equations Worksheet in Hindi
Chapter 05 Arithmetic Progression
CBSE Class 10 Arithmetic Progression Printable Worksheet Set A
CBSE Class 10 Arithmetic Progression Printable Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set A
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set C
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set D
CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set E
CBSE Class 10 Mental Maths Arithmetic Progressions Worksheet
CBSE Class 10 Mental Maths Arithmetic Progressions Worksheet in Hindi
Chapter 06 Triangles
CBSE Class 10 Mathematics Triangles Worksheet Set A
CBSE Class 10 Mathematics Triangles Worksheet Set B
CBSE Class 10 Mathematics Triangles Worksheet Set C
CBSE Class 10 Mathematics Triangles Worksheet Set D
CBSE Class 10 Mathematics Triangles Worksheet Set E
CBSE Class 10 Mental Maths Similar Triangles Worksheet
CBSE Class 10 Mental Maths Similar Triangles Worksheet in Hindi
Chapter 07 Coordinate Geometry
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set A
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E
CBSE Class 10 Mental Maths Coordinate Geometry Worksheet
CBSE Class 10 Mental Maths Coordinate Geometry Worksheet in Hindi
Chapter 08 Trigonometry
CBSE Class 10 Mathematics Trignometry Printable Worksheet Set B
CBSE Class 10 Mathematics Trignometry Printable Worksheet Set C
CBSE Class 10 Mathematics Trignometry Printable Worksheet Set D
CBSE Class 10 Mathematics Trignometry Printable Worksheet Set E
CBSE Class 10 Mathematics Trignometry Printable Worksheet Set F
CBSE Class 10 Trigonometry Printable Worksheet Set A
Chapter 09 Applications of Trigonometry
CBSE Class 10 Application of Trigonometry Worksheet Set B
CBSE Class 10 Mathematics Application of Trignometry Worksheet Set A
CBSE Class 10 Mathematics Application of Trignometry Worksheet Set B
CBSE Class 10 Mathematics Application of Trignometry Worksheet Set C
CBSE Class 10 Mental Maths Trigonometry And Its Applications Worksheet
CBSE Class 10 Mental Maths Trigonometry And Its Applications Worksheet in Hindi
Chapter 10 Circles
CBSE Class 10 Mathematics Circles Worksheet Set A
CBSE Class 10 Mathematics Circles Worksheet Set B
CBSE Class 10 Mathematics Circles Worksheet Set C
CBSE Class 10 Mathematics Circles Worksheet Set D
CBSE Class 10 Mathematics Circles Worksheet Set E
CBSE Class 10 Mathematics Circles Worksheet Set F
CBSE Class 10 Mathematics Circles Worksheet Set G
CBSE Class 10 Mental Maths Areas Related To Circle Worksheet
CBSE Class 10 Mental Maths Circle Worksheet
CBSE Class 10 Mental Maths Circle Worksheet in Hindi
Chapter 11 Construction
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet in Hindi
CBSE Class 10 Mental Maths Geometrical Constructions Worksheet Set A
Chapter 12 Areas related to Circles
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set A
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set B
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set C
CBSE Class 10 Mathematics Area Related To Circle Worksheet Set D
CBSE Class 10 Mental Maths Areas Related To Circle Worksheet in Hindi
Chapter 13 Surface Area and Volume
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set B
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set D
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set E
CBSE Class 10 Mental Maths Surface Areas And Volumes Worksheet
CBSE Class 10 Mental Maths Surface Areas And Volumes Worksheet in Hindi
Chapter 14 Statistics
CBSE Class 10 Mathematics Statistics Worksheet Set A
CBSE Class 10 Mathematics Statistics Worksheet Set B
CBSE Class 10 Mathematics Statistics Worksheet Set C
CBSE Class 10 Maths Statistics And Probabilty Worksheet
CBSE Class 10 Mental Maths Statistics And Probabilty Worksheet
CBSE Class 10 Mental Maths Statistics And Probabilty Worksheet in Hindi
Chapter 15 Probability
CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A
CBSE Class 10 Maths Probabilty Worksheet
z More Worksheets for Class 10 Mathematics
CBSE Class 10 Mathematics Question Bank
CBSE Class 10 Mathematics Worksheet Set A Solved
CBSE Class 10 Mathematics Worksheet Set B Solved
CBSE Class 10 Mathematics Worksheet Set C Solved
CBSE Class 10 Mathematics Worksheet Set D
CBSE Class 10 Mathematics Worksheet Set E
CBSE Class 10 Mathematics Worksheet Set F

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