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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 360 · 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 + 4y = −29 and 4x + y = −41 →
  2. 2.8x + y = 9 and x + 8y = −54 →
  3. 3.4x + 6y = 10 and 6x + 4y = 20 →
  4. 4.8x + 5y = 83 and 5x + 8y = 86 →
  5. 5.8x + 9y = −119 and 9x + 8y = −119 →
  6. 6.2x + 7y = 74 and 7x + 2y = 79 →
  7. 7.4x + 2y = 2 and 2x + 4y = −8 →
  8. 8.3x − 5y = 21 and x + 4y = −10 →
  9. 9.4x + 6y = −70 and 4x − 2y = −14 →
  10. 10.x + 9y = −39 and 9x + y = 49 →
  11. 11.6x + 3y = 45 and 3x − 3y = −9 →
  12. 12.5x − y = 35 and 2x + 2y = 26 →
  13. 13.4x − 2y = 28 and x − 4y = 14 →
  14. 14.3x + y = −15 and x + 3y = 3 →
  15. 15.6x + 2y = 36 and 2x − y = 7 →
  16. 16.2x + 3y = 35 and 3x + 2y = 35 →
  17. 17.7x + 4y = 91 and 4x + 7y = 85 →
  18. 18.2x + 4y = 48 and 3x + 4y = 56 →
  19. 19.2x + 6y = −46 and 2x − y = 10 →
  20. 20.x + 2y = 8 and 4x + 3y = 7 →
  21. 21.x + 6y = −35 and 4x + 2y = 14 →
  22. 22.9x + 2y = −70 and 2x + 9y = −7 →
  23. 23.6x + 3y = 54 and x − 2y = −6 →
  24. 24.5x − y = 22 and 6x − 4y = 32 →
  25. 25.x + 3y = 24 and 3x + y = 0 →
  26. 26.3x + 4y = 13 and 6x − 5y = 13 →
  27. 27.5x + 6y = −37 and 6x + 5y = −29 →
  28. 28.x − 2y = −13 and 5x + 5y = 70 →
  29. 29.3x − 5y = −11 and 2x + y = 10 →
  30. 30.3x + y = 19 and 5x + 2y = 33 →
  31. 31.3x + 4y = −19 and x + y = −7 →
  32. 32.6x + 6y = −30 and 4x − 6y = −50 →
  33. 33.5x + y = 27 and x + 2y = 0 →
  34. 34.4x + 6y = 62 and 6x + 4y = 48 →
  35. 35.3x − 3y = 18 and 6x + 5y = −19 →
  36. 36.4x + 3y = −6 and 3x − 3y = 27 →
  37. 37.5x + 2y = 39 and 2x + 5y = 24 →
  38. 38.4x + 3y = 27 and 3x + 5y = 12 →
  39. 39.x + 5y = 16 and 3x + y = −22 →
  40. 40.x + 2y = −3 and 3x + y = −14 →

Answer key

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

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