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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 141 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.x − y = 9 and 6x + y = 5 →
  2. 2.5x + y = 43 and 6x − y = 45 →
  3. 3.x − 4y = 9 and 5x + 4y = −51 →
  4. 4.x + 5y = 36 and 5x + y = −12 →
  5. 5.3x + 5y = 12 and 5x + 3y = −12 →
  6. 6.x + 5y = 50 and 4x + y = 29 →
  7. 7.x + 5y = −14 and 6x + 3y = −3 →
  8. 8.6x + y = 60 and x + 6y = 45 →
  9. 9.3x − 4y = 7 and 3x + 3y = −21 →
  10. 10.4x − 4y = −4 and x + 6y = 62 →
  11. 11.3x − 4y = −22 and 4x + 4y = 36 →
  12. 12.2x + 3y = 8 and 3x + 2y = 7 →
  13. 13.9x + 8y = 109 and 8x + 9y = 112 →
  14. 14.2x − 4y = 22 and x − 6y = 35 →
  15. 15.2x + 4y = −4 and 4x + 2y = 16 →
  16. 16.4x − 2y = 2 and 2x + 2y = −20 →
  17. 17.7x + 5y = 79 and 5x + 7y = 77 →
  18. 18.2x + 3y = −3 and 5x − 6y = 33 →
  19. 19.x + 2y = 23 and 3x + 5y = 60 →
  20. 20.5x + 3y = 48 and 4x + 3y = 39 →
  21. 21.4x − y = −38 and 3x − 5y = −37 →
  22. 22.2x + 3y = 16 and 4x − 4y = −8 →
  23. 23.2x + 6y = −58 and 4x + 6y = −74 →
  24. 24.2x + 5y = 12 and 5x + 2y = 9 →
  25. 25.6x + 6y = 12 and 4x + 3y = 5 →
  26. 26.3x + 5y = 26 and 2x + y = 1 →
  27. 27.7x + 4y = −2 and 4x + 7y = −20 →
  28. 28.4x − 2y = 12 and 4x + 4y = 48 →
  29. 29.8x + 6y = 44 and 6x + 8y = 54 →
  30. 30.x + 4y = 37 and 2x + 5y = 53 →
  31. 31.5x + y = 38 and 3x + y = 20 →
  32. 32.2x + 6y = −2 and 4x + y = 29 →
  33. 33.3x + 3y = 36 and 5x + 4y = 56 →
  34. 34.5x + 6y = −18 and 2x + 6y = −36 →
  35. 35.8x + 6y = 34 and 6x + 8y = 36 →
  36. 36.2x + 2y = 4 and 3x + y = 20 →
  37. 37.4x + 4y = −24 and x + 5y = −18 →
  38. 38.3x + 5y = −27 and 5x + 3y = −13 →
  39. 39.5x + y = 44 and x − 5y = −12 →
  40. 40.5x + 3y = −9 and 5x − 2y = 31 →

Answer key

  1. x = 2, y = −7
  2. x = 8, y = 3
  3. x = −7, y = −4
  4. x = −4, y = 8
  5. x = −6, y = 6
  6. x = 5, y = 9
  7. x = 1, y = −3
  8. x = 9, y = 6
  9. x = −3, y = −4
  10. x = 8, y = 9
  11. x = 2, y = 7
  12. x = 1, y = 2
  13. x = 5, y = 8
  14. x = −1, y = −6
  15. x = 6, y = −4
  16. x = −3, y = −7
  17. x = 7, y = 6
  18. x = 3, y = −3
  19. x = 5, y = 9
  20. x = 9, y = 1
  21. x = −9, y = 2
  22. x = 2, y = 4
  23. x = −8, y = −7
  24. x = 1, y = 2
  25. x = −1, y = 3
  26. x = −3, y = 7
  27. x = 2, y = −4
  28. x = 6, y = 6
  29. x = 1, y = 6
  30. x = 9, y = 7
  31. x = 9, y = −7
  32. x = 8, y = −3
  33. x = 8, y = 4
  34. x = 6, y = −8
  35. x = 2, y = 3
  36. x = 9, y = −7
  37. x = −3, y = −3
  38. x = 1, y = −6
  39. x = 8, y = 4
  40. x = 3, y = −8

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