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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 456 · 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. 1.2x + 6y = −22 and 5x + y = 15 →
  2. 2.5x − 6y = 14 and 5x − 2y = 18 →
  3. 3.4x + 2y = 20 and 2x + 4y = 22 →
  4. 4.6x + 4y = −8 and 3x + y = −8 →
  5. 5.5x − y = 4 and x + 6y = 7 →
  6. 6.8x + 6y = 0 and 6x + 8y = −14 →
  7. 7.5x + 4y = −12 and 3x − 4y = −52 →
  8. 8.6x + 3y = 66 and 3x + 6y = 60 →
  9. 9.6x + 4y = 80 and 6x − y = 40 →
  10. 10.6x + 6y = −30 and 6x + 3y = −12 →
  11. 11.9x + 2y = 23 and 2x + 9y = −12 →
  12. 12.6x + y = 12 and 3x + 6y = 39 →
  13. 13.7x + 8y = 31 and 8x + 7y = 29 →
  14. 14.2x − 3y = −23 and 6x − 3y = −15 →
  15. 15.2x − 4y = −12 and 3x + 6y = 6 →
  16. 16.9x + 4y = −6 and 4x + 9y = 19 →
  17. 17.5x − 5y = 0 and 6x + 6y = 84 →
  18. 18.3x + 4y = 10 and 4x + 3y = 11 →
  19. 19.3x + 2y = 6 and 2x + 3y = 19 →
  20. 20.5x + 3y = −45 and 3x + 5y = −43 →
  21. 21.5x − 2y = 19 and 4x + 5y = −31 →
  22. 22.9x + 2y = 97 and 2x + 9y = 90 →
  23. 23.6x + 4y = 8 and 4x + 6y = 2 →
  24. 24.4x + 9y = −21 and 9x + 4y = 34 →
  25. 25.2x + 6y = 14 and x − 6y = −11 →
  26. 26.3x − 4y = 7 and x + 6y = −49 →
  27. 27.7x + 2y = −5 and 2x + 7y = −40 →
  28. 28.3x + y = 32 and 4x + 3y = 51 →
  29. 29.4x + 4y = 36 and 6x + 4y = 46 →
  30. 30.2x + 2y = −2 and 3x − 6y = −48 →
  31. 31.x + 3y = −17 and 3x + y = −3 →
  32. 32.2x + 9y = −20 and 9x + 2y = 64 →
  33. 33.4x − 5y = 17 and x − y = 2 →
  34. 34.3x + 5y = 36 and 5x + 3y = 44 →
  35. 35.x + 9y = 59 and 9x + y = 51 →
  36. 36.2x + 3y = −3 and 4x − 5y = −39 →
  37. 37.x + 3y = 5 and x − y = 1 →
  38. 38.x − 4y = −13 and 5x + 2y = 1 →
  39. 39.5x + 2y = 19 and 2x + 5y = 37 →
  40. 40.x − 6y = −7 and 5x + y = 27 →

Answer key

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

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