WORKSHEET OF PAIR OF LINEAR EQUATIONS IN TWO VARIABLES CLASS-10
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I. MULTIPLE CHOICE QUESTIONS
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1. The pair of equations 5x – 15y = 8 and 3x – 9y = 24 / 5 has:
(a) one solutions
(b) two solutions
(c) infinitely many solutions
(d) no solution
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2. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is:
(a) 25
(b) 72
(c) 63
(d) 36
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3. Graphically, the pair of equations: 6x – 3y + 10 = 0; 2x – y + 9 = 0 represents two lines which are :
(a) intersecting at exactly one point
(b) intersecting at exactly two points
(c) coincident
(d) parallel
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4. The pair of equations x + 2y + 5 = 0 and
–3x – 6y + 1 = 0 have:
(a) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solution
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5. If a pair of linear equations is consistent, then the lines will be:
(a) parallel
(b) always coincident
(c) intersecting or coincident
(d) always intersecting
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6. The pair of equations y = 0 and y = –7 has :
(a) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution
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7. The pair of equations x = a and y = b graphically represents lines which are:
(a) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)
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8. For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?
(a) 1/ 2
(b) − 1/ 2
(c) 2
(d) –2
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9. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:
(a) −5 / 4
(b) 2 / 5
(c) 15 / 4
(d) 3 / 2
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10. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is:
(a) 3
(b) –3
(c) –12
(d) no value
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11. One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be:
(a) 10x + 14y + 4 = 0
(b) –10x – 14y + 4 = 0
(c) –10x + 14y + 4 = 0
(d) 10x – 14y = –4
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12. A pair of linear equations which has a unique solution x = 2, y = –3 is:
(a) x + y = 1, 2x – 3y = –5
(b) 2x + 5y = –11, 4x + 10y = –22
(c) 2x – y = 1, 3x + 2y = 0
(d) x – 4y – 14 = 0, 5x – y – 13 = 0
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13. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then values of a and b are, respectively :
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) –1 and –3
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14. Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Rs 1 and Rs 2 coins are, respectively :
(a) 35 and 15
(b) 35 and 20
(c) 15 and 35
(d) 25 and 25
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15. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are respectively:
(a) 4 and 24
(b) 5 and 30
(c) 6 and 36
(d) 3 and 24
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16. If 4x + 3y = 18xy and 2x – 5y + 4xy = 0, then values of x and y are :
(a) 1 / 2, 1 / 3
(b) 1 / 4 , 1/ 3
(c) − 1 / 2 ,1 / 3
(d) –1 and –3
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17. If a pair of linear equations is inconsistent then the lines representing these will be :
(a) parallel
(b) coincident
(c) intersecting or Concident
(d) intersecting
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18. The value of k, for which the pair of linear equations 4x + 6y – 1 = 0 and 2x – ky = 7 represents parallel lines is :
(a) 2
(b) –3
(c) 4
(d) –2
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19. If ax + by = a² – b² and bx + ay = 0, then the value of (x + y) is :
(a) a² – b²
(b) a + b
(c) a – b
(d) a² + b²
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20. If 88x + 36y = –92; 36x + 88y = –404, then :
(a) x = 1, y = –5
(b) x = 1, y = 5
(c) x = 2, y = –5
(d) x = –1, y = 5
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21. If 2 /x + 3/y = 13 and 5 /x - 4 / y = –2, then x + y =
(a) 1/ 6
(b) −1 /6
(c) 5 / 6
(d) 7/9
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22. x /a + y / b + = 2; ax – by = a² – b², then x / y =
(a) a² / b²
(b) a / b²
(c) a / b
(d) −a / b
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23. The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The value of x + y is :
(a) 110°
(b) 130°
(c) 140°
(d) 150°
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24. If the lines given by 3x + 2ky = 2 and 2x + 5y = –1 are parallel, then the value of k =
(a) 13 / 4
(b) 15 / 4
(c) 17 / 4
(d) 19 / 4
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25. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then a ÷ b = ?
(a) 1
(b) –2
(c) 2
(d) 3
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26. A number consists of two digits. The sum of the digits is 12 and the unit digit when divided by the tens digit gives the result as 3. The number is :
(a) 63
(b) 68
(c) 93
(d) 39
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27. Manisha scored x marks in Mathematics and y marks in Physics. The value of x and y, if x – y = 2 and xy = 2600 is :
(a) 50 and 52
(b) 68 and 26
(c) 51 and 54
(d) 36 and 52
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28. The length and breadth of a field if its area is 540 m² and perimeter is 96 m are :
(a) 36 m and 15 m
(b) 18 m and 30 m
(c) 9 m and 60 m
(d) 25 m and 21.6 m
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29. The values of x and y if 2x + y + 1 = 0 and 2x – 3y + 8 = 0, are :
(a) −11/ 8 ,7/ 4 ,
(b) 7 / 3 ,8 / 3 ,
(c) 15 / 7 , 9 / 11 ,
(d) −11/ 9 , 5 / 4 ,
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30. The values of x and y if 3x + 4y = 5 and 2x – 3y = 9 are :
(a) 3, –1
(b) 2, –1
(c) –2, –1
(d) –2, 1
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31. The values of x and y if 2x + 3y = 4 and 3x – y = –5, are :
(a) –1, –2
(b) –1, 2
(c) 1, –2
(d) 1, 2
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32. The values of x and y if 2x – 5y + 4 = 0 and 2x + y – 8 = 0, are :
(a) 1, 2
(b) 3, 2
(c) 2, 1
(d) 2, 3
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33. The values of x and y if 23x + 35y = 209 and 35x + 23y = 197, are :
(a) 3 and 4
(b) 4 and 5
(c) –3 and 2
(d) 5 and 3
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34. A fraction becomes 1/ 3 , if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator, it becomes 2 /5 . The fraction is :
(a) 2/ 7
(b) 3 /5
(c) 1 /7
(d) 5 /7
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35. For what value of b the point (3, b) lies on the line represented by 2x – 3y = 5?
(a) 1 / 2
(b) 1 / 3
(c) 1 / 5
(d) 1 / 7
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36. The values of x and y if 99x + 101y = 499 and 101x + 99y = 501 are :
(a) 3 and 2
(b) 5, 6
(c) –3 and 2
(d) –3 and –2
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37. For what value of k the system of linear equations kx + 3y = k – 2, 12x + ky = k has no solution?
(a) ± 2
(b) ± 3
(c) 1 / 5
(d) ± 6
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38. What is the point of intersection of the lines 3x + 7y = 12 and x-axis?
(a) (3, 0)
(b) (4, 0)
(c) (5, 0)
(d) (6, 0)
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39. For what value of k graphs of 4x – ky = 9 and 12x – 9y = 18 will be parallel?
(a) 1
(b) 2
(c) 3
(d) –3
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40. For what value of k, 2x + 3y = 4 and (k + 2)x + 6y = 3k + 2 will have infinitely many solutions?
(a) 5
(b) –5
(c) 2
(d) –2
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41. The values of x and y in (x + 2y - 4)/3 = (x+ y -3)/2 =( 3x + y)/11 are :
(a) 3 and 2
(b) 5 and 3
(c) 4 and 3
(d) 5 and –3
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42. For what values of a and b does the following pair of equations have an infinite number of solutions? 2x + 3y = 7; a(x + y) – b (x – y) = 3a + b – 2
(a) 3 and 1
(b) 5 and 1
(c) 4 and 3
(d) 5 and –2
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43. In a competitive examination, 1 mark is awarded for each correct answer, while 1 / 2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. Number of questions she attempted correctly is :
(a) 96
(b) 98
(c) 100
(d) 105
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44. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, then the numbers are :
(a) 25 and 30
(b) 40 and 48
(c) 30 and 36
(d) 45 and 54
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45. For what values of p and q the system of equations, 2x + 3y = 7; (p + q + 1)x + (p + 2q + 2)y = 4 (p + q) + 1 will represent coincident lines ?
(a) 1, 5
(b) 3, 5
(c) 4, 3
(d) 3, 2
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46. The value of k for which the given system of equations 3x + y = 1 and (2k – 1)x + (k – 1)y = 5 has no solution is :
(a) 1
(b) 2
(c) 3
(d) 4
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47. The value of α for which αx + 3y = α – 3 and 12x + αy = α has no solutions :
(a) –5
(b) –6
(c) 6
(d) 7
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48. The sum of two numbers is 15 and the sum of their reciprocals is 3 /10 . The numbers are:
(a) 9, 6
(b) 12, 3
(c) 11, 4
(d) 5, 10
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49. The values of x and y in 4 /x + 5y = 7 and 3 /x + 4y = 5 are :
(a) 1/ 2 , 1
(b) 1 /3 , –1
(c) 1/ 3 , 2
(d) 5/ 2 ,3
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50. The values for x and y in 4/ x + 3y = 8 and 6/ x – 4y = –5 are :
(a) 2, 2
(b) 3, 3
(c) 1, 1
(d) 4, 4
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II. FILL IN THE BLANKS
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1. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is ___________.
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2. If 4x + 3y = 18xy and 2x – 5y + 4xy = 0, then values of x and y will be respectively ____________ and ____________.
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3. If ax + by = a² – b² and bx + ay = 0, then value of (x + y) = __________.
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4. The value of k, for which the pair of linear equations 4x + 6y – 1 = 0 and 2x – ky = 7 represents parallel lines is _________.
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5. Values of a and b for which the pair of linear equations x + 2y = 1; (a – b)x + (a + b)y = a + b – 2, have infinitely many solutions are ___________ and ___________.
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6. If 37x + 43y = 123 and 43x + 37y = 117 then x + y = ____________.
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7. 15 years hence a man will be just 4 times as old as he was 15 years ago. His present age is ___________.
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8. The value of k for which the system of equations kx + 2y = 5, 3x + 4y = 1, has no solution is ____________.
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9. A number consists of two digits whose sum is 15. If 9 is added to the number, then the digits change their places. The number is ____________.
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10. The difference between two numbers is 26 and one number is three times the other. The numbers are ____________.
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11. The larger of two supplementary angles exceeds the smaller by 18 degrees. The angles are ______________.
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12. The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. The cost of each bat and each ball is ____________.
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13. A fraction becomes 9 / 11 , if 2 is added to both the numerator and the denomirator. If 3 is added to both numerator and denominator it becomes 5/6 . The fraction is __________.
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14. If 4/ x + 3y = 14; 3 /x – 4y = 23, then x × y = ____________.
15. In ∆ABC, if ∠C = 3 ∠B = 2 (∠A + ∠B), then ∠A = _____, ∠B = _____, ∠C = _____.
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III. VERY SHORT ANSWER QUESTIONS
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1. Write the standard form of an equation in two variables.
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2. At most how many solutions can a linear equation in two variable have?
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3. The graphs of two linear equations in two variables intersect at a point. What does it mean?
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4. Write two equations of lines which are concident with 2x + 3y = 9.
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5. In the equations a1x + b1 y = c1 = 0 and a2x + b2y + c2 = 0 if a1 / a2 not 🚭 b1/ b2 , then the equations with represent intersecting lines. Is it true?
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6. The graphical representation of the pair of equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 represents intersecting lines. Is it true?
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7. For what value of k do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?
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8. Find the value of k for which the pair of linear equations 4x + 6y = 1 and 2x + ky – 7 = 0 represent parallel lines.
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