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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 578 · 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 + 2y = 4 and 6x + 4y = 16 →
  2. 2.5x + 6y = 26 and 6x + y = 25 →
  3. 3.3x + 6y = 66 and 6x + 3y = 51 →
  4. 4.7x + 8y = 91 and 8x + 7y = 89 →
  5. 5.5x + 2y = 9 and x − 4y = −7 →
  6. 6.4x + 6y = 42 and 4x − y = 7 →
  7. 7.2x + 3y = 31 and 5x + 2y = 50 →
  8. 8.2x + y = −4 and 4x − y = −32 →
  9. 9.9x + 5y = 54 and 5x + 9y = 86 →
  10. 10.8x + 7y = −4 and 7x + 8y = −11 →
  11. 11.x + 6y = 38 and 2x + 6y = 40 →
  12. 12.6x + 5y = 54 and 5x + 6y = 56 →
  13. 13.x + 8y = 66 and 8x + y = 24 →
  14. 14.x − 2y = 5 and 4x + 2y = −20 →
  15. 15.4x + 5y = 41 and 5x − 4y = 0 →
  16. 16.x + 3y = −11 and 5x − y = 9 →
  17. 17.x − y = −1 and 3x − 6y = −15 →
  18. 18.5x + 9y = −52 and 9x + 5y = −4 →
  19. 19.3x + 5y = −19 and 6x + 3y = −45 →
  20. 20.x − 4y = −30 and 2x + y = 12 →
  21. 21.6x + 3y = 27 and 3x + 6y = 9 →
  22. 22.5x + y = 45 and x + 5y = 33 →
  23. 23.x − 4y = −26 and 4x + y = 15 →
  24. 24.x − 5y = −40 and x + 4y = 41 →
  25. 25.9x + 4y = 56 and 4x + 9y = −4 →
  26. 26.3x + 4y = 3 and 4x + 3y = 18 →
  27. 27.x + 9y = 71 and 9x + y = 79 →
  28. 28.4x + 5y = 43 and 6x + 3y = 33 →
  29. 29.4x + 6y = 62 and 5x + 4y = 46 →
  30. 30.6x + 6y = 24 and 6x + 5y = 18 →
  31. 31.3x + 4y = −3 and 4x + 3y = −18 →
  32. 32.3x + 5y = −35 and 4x − 6y = 4 →
  33. 33.9x + 4y = 80 and 4x + 9y = 50 →
  34. 34.6x + 6y = 48 and 6x − y = 27 →
  35. 35.3x − y = 7 and 3x + 6y = 0 →
  36. 36.3x + y = 1 and 6x + y = 7 →
  37. 37.x − 3y = −24 and 6x + 5y = 63 →
  38. 38.3x − y = 19 and 4x + 2y = 42 →
  39. 39.x + y = 1 and 3x + y = 9 →
  40. 40.2x + 4y = 20 and 4x + 5y = 31 →

Answer key

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

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