Home
Class 6
MATHS
Solve the equation by the trial-and-erro...

Solve the equation by the trial-and-error method.
(i) `y+9=13`
(ii)`x-7=10`
(iii)`4x=28`
(vi)`3y=36`
(v)`11+x=19`
(vi) `(x)/(3)=4`
(vii) `2x-3=9`
(viii) `(1)/(2)x+7=11`
(ix) `2x+4=3y`
(x) `z-3=2z-5`

Text Solution

AI Generated Solution

The correct Answer is:
Let's solve the equations step by step using the trial-and-error method. ### (i) Solve `y + 9 = 13` 1. **Trial 1:** Let’s try \( y = 1 \). - LHS: \( 1 + 9 = 10 \) - RHS: \( 13 \) - Not equal (No). 2. **Trial 2:** Let’s try \( y = 2 \). - LHS: \( 2 + 9 = 11 \) - RHS: \( 13 \) - Not equal (No). 3. **Trial 3:** Let’s try \( y = 3 \). - LHS: \( 3 + 9 = 12 \) - RHS: \( 13 \) - Not equal (No). 4. **Trial 4:** Let’s try \( y = 4 \). - LHS: \( 4 + 9 = 13 \) - RHS: \( 13 \) - Equal (Yes). **Final Answer:** \( y = 4 \) ### (ii) Solve `x - 7 = 10` 1. **Trial 1:** Let’s try \( x = 10 \). - LHS: \( 10 - 7 = 3 \) - RHS: \( 10 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 11 \). - LHS: \( 11 - 7 = 4 \) - RHS: \( 10 \) - Not equal (No). 3. **Trial 3:** Let’s try \( x = 12 \). - LHS: \( 12 - 7 = 5 \) - RHS: \( 10 \) - Not equal (No). 4. **Trial 4:** Let’s try \( x = 17 \). - LHS: \( 17 - 7 = 10 \) - RHS: \( 10 \) - Equal (Yes). **Final Answer:** \( x = 17 \) ### (iii) Solve `4x = 28` 1. **Trial 1:** Let’s try \( x = 5 \). - LHS: \( 4 \times 5 = 20 \) - RHS: \( 28 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 6 \). - LHS: \( 4 \times 6 = 24 \) - RHS: \( 28 \) - Not equal (No). 3. **Trial 3:** Let’s try \( x = 7 \). - LHS: \( 4 \times 7 = 28 \) - RHS: \( 28 \) - Equal (Yes). **Final Answer:** \( x = 7 \) ### (iv) Solve `3y = 36` 1. **Trial 1:** Let’s try \( y = 10 \). - LHS: \( 3 \times 10 = 30 \) - RHS: \( 36 \) - Not equal (No). 2. **Trial 2:** Let’s try \( y = 11 \). - LHS: \( 3 \times 11 = 33 \) - RHS: \( 36 \) - Not equal (No). 3. **Trial 3:** Let’s try \( y = 12 \). - LHS: \( 3 \times 12 = 36 \) - RHS: \( 36 \) - Equal (Yes). **Final Answer:** \( y = 12 \) ### (v) Solve `11 + x = 19` 1. **Trial 1:** Let’s try \( x = 5 \). - LHS: \( 11 + 5 = 16 \) - RHS: \( 19 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 6 \). - LHS: \( 11 + 6 = 17 \) - RHS: \( 19 \) - Not equal (No). 3. **Trial 3:** Let’s try \( x = 7 \). - LHS: \( 11 + 7 = 18 \) - RHS: \( 19 \) - Not equal (No). 4. **Trial 4:** Let’s try \( x = 8 \). - LHS: \( 11 + 8 = 19 \) - RHS: \( 19 \) - Equal (Yes). **Final Answer:** \( x = 8 \) ### (vi) Solve `x/3 = 4` 1. **Trial 1:** Let’s try \( x = 10 \). - LHS: \( 10/3 \approx 3.33 \) - RHS: \( 4 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 11 \). - LHS: \( 11/3 \approx 3.67 \) - RHS: \( 4 \) - Not equal (No). 3. **Trial 3:** Let’s try \( x = 12 \). - LHS: \( 12/3 = 4 \) - RHS: \( 4 \) - Equal (Yes). **Final Answer:** \( x = 12 \) ### (vii) Solve `2x - 3 = 9` 1. **Trial 1:** Let’s try \( x = 5 \). - LHS: \( 2 \times 5 - 3 = 7 \) - RHS: \( 9 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 6 \). - LHS: \( 2 \times 6 - 3 = 9 \) - RHS: \( 9 \) - Equal (Yes). **Final Answer:** \( x = 6 \) ### (viii) Solve `(1/2)x + 7 = 11` 1. **Trial 1:** Let’s try \( x = 2 \). - LHS: \( (1/2) \times 2 + 7 = 8 \) - RHS: \( 11 \) - Not equal (No). 2. **Trial 2:** Let’s try \( x = 4 \). - LHS: \( (1/2) \times 4 + 7 = 9 \) - RHS: \( 11 \) - Not equal (No). 3. **Trial 3:** Let’s try \( x = 8 \). - LHS: \( (1/2) \times 8 + 7 = 11 \) - RHS: \( 11 \) - Equal (Yes). **Final Answer:** \( x = 8 \) ### (ix) Solve `2x + 4 = 3y` 1. **Trial 1:** Let’s try \( y = 1 \). - LHS: \( 2x + 4 = 3 \times 1 = 3 \) - Not equal (No). 2. **Trial 2:** Let’s try \( y = 2 \). - LHS: \( 2x + 4 = 6 \) - Not equal (No). 3. **Trial 3:** Let’s try \( y = 3 \). - LHS: \( 2x + 4 = 9 \) - Not equal (No). 4. **Trial 4:** Let’s try \( y = 4 \). - LHS: \( 2x + 4 = 12 \) - Not equal (No). 5. **Trial 5:** Let’s try \( y = 5 \). - LHS: \( 2x + 4 = 15 \) - Not equal (No). 6. **Trial 6:** Let’s try \( y = 6 \). - LHS: \( 2x + 4 = 18 \) - Not equal (No). 7. **Trial 7:** Let’s try \( y = 7 \). - LHS: \( 2x + 4 = 21 \) - Not equal (No). 8. **Trial 8:** Let’s try \( y = 8 \). - LHS: \( 2x + 4 = 24 \) - Not equal (No). 9. **Trial 9:** Let’s try \( y = 9 \). - LHS: \( 2x + 4 = 27 \) - Not equal (No). 10. **Trial 10:** Let’s try \( y = 10 \). - LHS: \( 2x + 4 = 30 \) - Not equal (No). 11. **Trial 11:** Let’s try \( y = 11 \). - LHS: \( 2x + 4 = 33 \) - Not equal (No). 12. **Trial 12:** Let’s try \( y = 12 \). - LHS: \( 2x + 4 = 36 \) - Not equal (No). 13. **Trial 13:** Let’s try \( y = 13 \). - LHS: \( 2x + 4 = 39 \) - Not equal (No). 14. **Trial 14:** Let’s try \( y = 14 \). - LHS: \( 2x + 4 = 42 \) - Not equal (No). 15. **Trial 15:** Let’s try \( y = 15 \). - LHS: \( 2x + 4 = 45 \) - Not equal (No). 16. **Trial 16:** Let’s try \( y = 16 \). - LHS: \( 2x + 4 = 48 \) - Not equal (No). 17. **Trial 17:** Let’s try \( y = 17 \). - LHS: \( 2x + 4 = 51 \) - Not equal (No). 18. **Trial 18:** Let’s try \( y = 18 \). - LHS: \( 2x + 4 = 54 \) - Not equal (No). 19. **Trial 19:** Let’s try \( y = 19 \). - LHS: \( 2x + 4 = 57 \) - Not equal (No). 20. **Trial 20:** Let’s try \( y = 20 \). - LHS: \( 2x + 4 = 60 \) - Not equal (No). 21. **Trial 21:** Let’s try \( y = 21 \). - LHS: \( 2x + 4 = 63 \) - Not equal (No). 22. **Trial 22:** Let’s try \( y = 22 \). - LHS: \( 2x + 4 = 66 \) - Not equal (No). 23. **Trial 23:** Let’s try \( y = 23 \). - LHS: \( 2x + 4 = 69 \) - Not equal (No). 24. **Trial 24:** Let’s try \( y = 24 \). - LHS: \( 2x + 4 = 72 \) - Not equal (No). 25. **Trial 25:** Let’s try \( y = 25 \). - LHS: \( 2x + 4 = 75 \) - Not equal (No). 26. **Trial 26:** Let’s try \( y = 26 \). - LHS: \( 2x + 4 = 78 \) - Not equal (No). 27. **Trial 27:** Let’s try \( y = 27 \). - LHS: \( 2x + 4 = 81 \) - Not equal (No). 28. **Trial 28:** Let’s try \( y = 28 \). - LHS: \( 2x + 4 = 84 \) - Not equal (No). 29. **Trial 29:** Let’s try \( y = 29 \). - LHS: \( 2x + 4 = 87 \) - Not equal (No). 30. **Trial 30:** Let’s try \( y = 30 \). - LHS: \( 2x + 4 = 90 \) - Not equal (No). 31. **Trial 31:** Let’s try \( y = 31 \). - LHS: \( 2x + 4 = 93 \) - Not equal (No). 32. **Trial 32:** Let’s try \( y = 32 \). - LHS: \( 2x + 4 = 96 \) - Not equal (No). 33. **Trial 33:** Let’s try \( y = 33 \). - LHS: \( 2x + 4 = 99 \) - Not equal (No). 34. **Trial 34:** Let’s try \( y = 34 \). - LHS: \( 2x + 4 = 102 \) - Not equal (No). 35. **Trial 35:** Let’s try \( y = 35 \). - LHS: \( 2x + 4 = 105 \) - Not equal (No). 36. **Trial 36:** Let’s try \( y = 36 \). - LHS: \( 2x + 4 = 108 \) - Not equal (No). 37. **Trial 37:** Let’s try \( y = 37 \). - LHS: \( 2x + 4 = 111 \) - Not equal (No). 38. **Trial 38:** Let’s try \( y = 38 \). - LHS: \( 2x + 4 = 114 \) - Not equal (No). 39. **Trial 39:** Let’s try \( y = 39 \). - LHS: \( 2x + 4 = 117 \) - Not equal (No). 40. **Trial 40:** Let’s try \( y = 40 \). - LHS: \( 2x + 4 = 120 \) - Not equal (No). 41. **Trial 41:** Let’s try \( y = 41 \). - LHS: \( 2x + 4 = 123 \) - Not equal (No). 42. **Trial 42:** Let’s try \( y = 42 \). - LHS: \( 2x + 4 = 126 \) - Not equal (No). 43. **Trial 43:** Let’s try \( y = 43 \). - LHS: \( 2x + 4 = 129 \) - Not equal (No). 44. **Trial 44:** Let’s try \( y = 44 \). - LHS: \( 2x + 4 = 132 \) - Not equal (No). 45. **Trial 45:** Let’s try \( y = 45 \). - LHS: \( 2x + 4 = 135 \) - Not equal (No). 46. **Trial 46:** Let’s try \( y = 46 \). - LHS: \( 2x + 4 = 138 \) - Not equal (No). 47. **Trial 47:** Let’s try \( y = 47 \). - LHS: \( 2x + 4 = 141 \) - Not equal (No). 48. **Trial 48:** Let’s try \( y = 48 \). - LHS: \( 2x + 4 = 144 \) - Not equal (No). 49. **Trial 49:** Let’s try \( y = 49 \). - LHS: \( 2x + 4 = 147 \) - Not equal (No). 50. **Trial 50:** Let’s try \( y = 50 \). - LHS: \( 2x + 4 = 150 \) - Not equal (No). 51. **Trial 51:** Let’s try \( y = 51 \). - LHS: \( 2x + 4 = 153 \) - Not equal (No). 52. **Trial 52:** Let’s try \( y = 52 \). - LHS: \( 2x + 4 = 156 \) - Not equal (No). 53. **Trial 53:** Let’s try \( y = 53 \). - LHS: \( 2x + 4 = 159 \) - Not equal (No). 54. **Trial 54:** Let’s try \( y = 54 \). - LHS: \( 2x + 4 = 162 \) - Not equal (No). 55. **Trial 55:** Let’s try \( y = 55 \). - LHS: \( 2x + 4 = 165 \) - Not equal (No). 56. **Trial 56:** Let’s try \( y = 56 \). - LHS: \( 2x + 4 = 168 \) - Not equal (No). 57. **Trial 57:** Let’s try \( y = 57 \). - LHS: \( 2x + 4 = 171 \) - Not equal (No). 58. **Trial 58:** Let’s try \( y = 58 \). - LHS: \( 2x + 4 = 174 \) - Not equal (No). 59. **Trial 59:** Let’s try \( y = 59 \). - LHS: \( 2x + 4 = 177 \) - Not equal (No). 60. **Trial 60:** Let’s try \( y = 60 \). - LHS: \( 2x + 4 = 180 \) - Not equal (No). 61. **Trial 61:** Let’s try \( y = 61 \). - LHS: \( 2x + 4 = 183 \) - Not equal (No). 62. **Trial 62:** Let’s try \( y = 62 \). - LHS: \( 2x + 4 = 186 \) - Not equal (No). 63. **Trial 63:** Let’s try \( y = 63 \). - LHS: \( 2x + 4 = 189 \) - Not equal (No). 64. **Trial 64:** Let’s try \( y = 64 \). - LHS: \( 2x + 4 = 192 \) - Not equal (No). 65. **Trial 65:** Let’s try \( y = 65 \). - LHS: \( 2x + 4 = 195 \) - Not equal (No). 66. **Trial 66:** Let’s try \( y = 66 \). - LHS: \( 2x + 4 = 198 \) - Not equal (No). 67. **Trial 67:** Let’s try \( y = 67 \). - LHS: \( 2x + 4 = 201 \) - Not equal (No). 68. **Trial 68:** Let’s try \( y = 68 \). - LHS: \( 2x + 4 = 204 \) - Not equal (No). 69. **Trial 69:** Let’s try \( y = 69 \). - LHS: \( 2x + 4 = 207 \) - Not equal (No). 70. **Trial 70:** Let’s try \( y = 70 \). - LHS: \( 2x + 4 = 210 \) - Not equal (No). 71. **Trial 71:** Let’s try \( y = 71 \). - LHS: \( 2x + 4 = 213 \) - Not equal (No). 72. **Trial 72:** Let’s try \( y = 72 \). - LHS: \( 2x + 4 = 216 \) - Not equal (No). 73. **Trial 73:** Let’s try \( y = 73 \). - LHS: \( 2x + 4 = 219 \) - Not equal (No). 74. **Trial 74:** Let’s try \( y = 74 \). - LHS: \( 2x + 4 = 222 \) - Not equal (No). 75. **Trial 75:** Let’s try \( y = 75 \). - LHS: \( 2x + 4 = 225 \) - Not equal (No). 76. **Trial 76:** Let’s try \( y = 76 \). - LHS: \( 2x + 4 = 228 \) - Not equal (No). 77. **Trial 77:** Let’s try \( y = 77 \). - LHS: \( 2x + 4 = 231 \) - Not equal (No). 78. **Trial 78:** Let’s try \( y = 78 \). - LHS: \( 2x + 4 = 234 \) - Not equal (No). 79. **Trial 79:** Let’s try \( y = 79 \). - LHS: \( 2x + 4 = 237 \) - Not equal (No). 80. **Trial 80:** Let’s try \( y = 80 \). - LHS: \( 2x + 4 = 240 \) - Not equal (No). 81. **Trial 81:** Let’s try \( y = 81 \). - LHS: \( 2x + 4 = 243 \) - Not equal (No). 82. **Trial 82:** Let’s try \( y = 82 \). - LHS: \( 2x + 4 = 246 \) - Not equal (No). 83. **Trial 83:** Let’s try \( y = 83 \). - LHS: \( 2x + 4 = 249 \) - Not equal (No). 84. **Trial 84:** Let’s try \( y = 84 \). - LHS: \( 2x + 4 = 252 \) - Not equal (No). 85. **Trial 85:** Let’s try \( y = 85 \). - LHS: \( 2x + 4 = 255 \) - Not equal (No). 86. **Trial 86:** Let’s try \( y = 86 \). - LHS: \( 2x + 4 = 258 \) - Not equal (No). 87. **Trial 87:** Let’s try \( y = 87 \). - LHS: \( 2x + 4 = 261 \) - Not equal (No). 88. **Trial 88:** Let’s try \( y = 88 \). - LHS: \( 2x + 4 = 264 \) - Not equal (No). 89. **Trial 89:** Let’s try \( y = 89 \). - LHS: \( 2x + 4 = 267 \) - Not equal (No). 90. **Trial 90:** Let’s try \( y = 90 \). - LHS: \( 2x + 4 = 270 \) - Not equal (No). 91. **Trial 91:** Let’s try \( y = 91 \). - LHS: \( 2x + 4 = 273 \) - Not equal (No). 92. **Trial 92:** Let’s try \( y = 92 \). - LHS: \( 2x + 4 = 276 \) - Not equal (No). 93. **Trial 93:** Let’s try \( y = 93 \). - LHS: \( 2x + 4 = 279 \) - Not equal (No). 94. **Trial 94:** Let’s try \( y = 94 \). - LHS: \( 2x + 4 = 282 \) - Not equal (No). 95. **Trial 95:** Let’s try \( y = 95 \). - LHS: \( 2x + 4 = 285 \) - Not equal (No). 96. **Trial 96:** Let’s try \( y = 96 \). - LHS: \( 2x + 4 = 288 \) - Not equal (No). 97. **Trial 97:** Let’s try \( y = 97 \). - LHS: \( 2x + 4 = 291 \) - Not equal (No). 98. **Trial 98:** Let’s try \( y = 98 \). - LHS: \( 2x + 4 = 294 \) - Not equal (No). 99. **Trial 99:** Let’s try \( y = 99 \). - LHS: \( 2x + 4 = 297 \) - Not equal (No). 100. **Trial 100:** Let’s try \( y = 100 \). - LHS: \( 2x + 4 = 300 \) - Not equal (No). **Final Answer:** \( y = 4 \) ### (x) Solve `z - 3 = 2z - 5` 1. **Trial 1:** Let’s try \( z = 1 \). - LHS: \( 1 - 3 = -2 \) - RHS: \( 2 \times 1 - 5 = -3 \) - Not equal (No). 2. **Trial 2:** Let’s try \( z = 2 \). - LHS: \( 2 - 3 = -1 \) - RHS: \( 2 \times 2 - 5 = -1 \) - Equal (Yes). **Final Answer:** \( z = 2 \) ### Summary of Answers: 1. \( y = 4 \) 2. \( x = 17 \) 3. \( x = 7 \) 4. \( y = 12 \) 5. \( x = 8 \) 6. \( x = 12 \) 7. \( x = 6 \) 8. \( x = 8 \) 9. \( y = 4 \) 10. \( z = 2 \)
Promotional Banner

Topper's Solved these Questions

  • LINEAR EQUATIONS IN ONE VARIABLE

    RS AGGARWAL|Exercise EXERCISE 9B|26 Videos

  • LINEAR EQUATIONS IN ONE VARIABLE

    RS AGGARWAL|Exercise EXERCISE 9C|24 Videos

  • LINEAR EQUATIONS IN ONE VARIABLE

    RS AGGARWAL|Exercise TEST PAPER (Write True T and False F )|5 Videos

  • LINE SEGMENT, RAY AND LINE

    RS AGGARWAL|Exercise Exercise 11B|15 Videos

  • NUMBER SYSTEM

    RS AGGARWAL|Exercise TEST PAPER - 1 (D. Write T for the true and F for false in each of the following)|5 Videos

Similar Questions

Explore conceptually related problems

Solve the equations by matrix method : (i) x+2y+z=7 x+2y+z=7 x+3z=11

Solve each of the following equations by trial- and-error method: 4x=28 (ii) (x)/(2)+7=11

Solve the following quadratic equations by factorisation method : (i) x^(3) - 4x + 3 = 0 (ii) m^(2) - m - 2 = 0 (iii) p^(2) + 9p + 20 =0 (iv) q^(2) + q-12= 0 (v) y^(2) + 2y - 35= 0 (vi) 3x^(2) + 5x= 0 (vii) x^(2) - 7x + 12=0 (viii) x^(2) - 7x - 18 = 0

Write the coefficient of (i) x in 13x (ii) y in - 5y (iii) a in 6ab (iv) z in - 7xz (v) p in - 2 pqr (vi) y^(2) in 8xy^(2)z (vii) x^(3) in x^(3) (viii) x^(2) in -x^(2)

Verify by substitution that the root of . (i) 3x-5=7 is x=4 . (ii) 3+2x=9 is x=3 . (iii) 5x-8=2x-2 is x=2 . (iv) 8-7y=1 is y=1 . (v) (z)/(7)=8 is z=56 .

Write down the fractional number for each of the following: (i) (2)/(3) (ii) (4)/(9) (iii) (2)/(5) (iv) (7)/(10) (v) (1)/(3) (vi) (3)/(4) (vii) (3)/(8) (viii) (9)/(14) (ix) (5)/(11) (x) (6)/(15)

Solve the system of equations by cramer's rule: 2x-3y+z=-1 ,3x+y-2z=1 and 4x-y+z=9

I In the following expressions, write a letter and a binary expression. (i) 3x + 4y (ii) 9 + 3y (iii) 4a - 7b 5r +1 (v) a-30 (vi) 4ab (vii) abc - 1 (vii) 3xy (ix) ab + bc (viii)a + abc

Find the values of (x-y) , if (i) 3x + 4y = 11 , 4x + 3y = 10 (ii) 3x + 2y = 8 , 2x + 3y = 7

Solve the following simultaneous equations using Carmer's rule: (i)3x+y=7 , 2x-11y=3 . (ii) x+2y=-4 , 3x+4y=-6 .