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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 622 · 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 + 6y = 8 and 2x + y = 5 →
  2. 2.2x + 6y = 6 and 2x + 2y = −6 →
  3. 3.9x + 2y = 10 and 2x + 9y = −32 →
  4. 4.x + 8y = 57 and 8x + y = 78 →
  5. 5.6x − y = 24 and x + 2y = 17 →
  6. 6.3x + 9y = −3 and 9x + 3y = 63 →
  7. 7.5x − y = −26 and 5x + 3y = −42 →
  8. 8.2x + 8y = −52 and 8x + 2y = 2 →
  9. 9.4x + 2y = 16 and 4x − y = 10 →
  10. 10.3x − 2y = 7 and 6x − 2y = 22 →
  11. 11.6x + 3y = 36 and 3x + 6y = 54 →
  12. 12.3x − 3y = −3 and 4x + 3y = −11 →
  13. 13.5x + 4y = 6 and 2x + 2y = 2 →
  14. 14.5x + 3y = −14 and 3x + 3y = −6 →
  15. 15.7x + 9y = 61 and 9x + 7y = 51 →
  16. 16.3x + 5y = 28 and x − 3y = −14 →
  17. 17.5x − y = 12 and 3x − 6y = 18 →
  18. 18.5x + 4y = 49 and 2x + y = 19 →
  19. 19.2x + 6y = −16 and 6x + 2y = 0 →
  20. 20.3x − 2y = 8 and 4x + 4y = 4 →
  21. 21.x + 4y = 1 and 4x + y = 19 →
  22. 22.3x + 4y = 17 and 4x + 3y = 11 →
  23. 23.9x + 5y = 96 and 5x + 9y = 72 →
  24. 24.x − 2y = −10 and 4x + 6y = 44 →
  25. 25.6x + 4y = 52 and 4x + 5y = 37 →
  26. 26.2x + 7y = −8 and 7x + 2y = 17 →
  27. 27.3x + 6y = 63 and x + 5y = 45 →
  28. 28.2x − 2y = −18 and 5x + 3y = −29 →
  29. 29.2x − 2y = −32 and 2x − 6y = −68 →
  30. 30.2x + 3y = 30 and 3x + 2y = 30 →
  31. 31.2x + y = 18 and x + 2y = 12 →
  32. 32.3x + 4y = 60 and 4x + 3y = 59 →
  33. 33.x − 3y = −13 and 2x + y = −12 →
  34. 34.4x + 7y = −40 and 7x + 4y = −4 →
  35. 35.8x + 9y = 57 and 9x + 8y = 62 →
  36. 36.x + 7y = −1 and 7x + y = −55 →
  37. 37.5x + y = 32 and x + 5y = −8 →
  38. 38.4x + 3y = 1 and 3x + 4y = −15 →
  39. 39.2x + 4y = 32 and 4x + 2y = 28 →
  40. 40.6x + 3y = 30 and 3x + 6y = 42 →

Answer key

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

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