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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 17 · 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. 1.4x + 4y = −16 and 3x + y = −6 →
  2. 2.4x + 9y = 91 and 9x + 4y = 91 →
  3. 3.5x + 9y = 43 and 9x + 5y = 55 →
  4. 4.4x + 6y = 44 and 4x − 5y = 0 →
  5. 5.x + 9y = 12 and 9x + y = −52 →
  6. 6.x − 6y = 58 and 4x − 4y = 52 →
  7. 7.2x + 5y = 45 and 3x − 3y = −6 →
  8. 8.2x − 6y = −6 and 2x + 5y = 38 →
  9. 9.5x − 2y = −13 and 5x + 3y = 32 →
  10. 10.2x + 3y = 18 and x + y = 5 →
  11. 11.4x + 2y = 12 and 5x − 3y = 4 →
  12. 12.x − 4y = 31 and 5x + 2y = 1 →
  13. 13.7x + 6y = 40 and 6x + 7y = 38 →
  14. 14.9x + 2y = 54 and 2x + 9y = 89 →
  15. 15.6x − 6y = 72 and 3x + 6y = −45 →
  16. 16.5x + 6y = 61 and x + 3y = 23 →
  17. 17.4x − y = 31 and 5x + 3y = 26 →
  18. 18.5x + 7y = −16 and 7x + 5y = −32 →
  19. 19.x + y = −2 and 5x − 5y = −20 →
  20. 20.8x + 3y = 62 and 3x + 8y = 37 →
  21. 21.5x + 3y = −54 and 3x + 5y = −58 →
  22. 22.3x − y = 28 and 6x − y = 52 →
  23. 23.5x − 3y = 24 and 6x − 2y = 40 →
  24. 24.2x + 4y = 38 and 3x + y = 27 →
  25. 25.5x + 9y = 116 and 9x + 5y = 108 →
  26. 26.6x + y = 9 and x + 6y = −51 →
  27. 27.8x + 6y = 48 and 6x + 8y = 50 →
  28. 28.4x + 3y = 45 and 4x − y = 33 →
  29. 29.9x + 6y = 75 and 6x + 9y = 75 →
  30. 30.x + 2y = 23 and 6x + y = 50 →
  31. 31.6x − 3y = −45 and 3x + 5y = −3 →
  32. 32.6x + 5y = −2 and 2x + 6y = 8 →
  33. 33.7x + 3y = 80 and 3x + 7y = 80 →
  34. 34.4x − 2y = −14 and 5x + 3y = −23 →
  35. 35.6x + 3y = 48 and 3x + 6y = 51 →
  36. 36.2x − 3y = −39 and x + y = 3 →
  37. 37.x + 2y = −3 and 6x + 6y = −6 →
  38. 38.3x + 6y = 27 and x + 4y = 15 →
  39. 39.5x + 3y = −16 and 6x + 4y = −18 →
  40. 40.x + 6y = −53 and 4x + 3y = −44 →

Answer key

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

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