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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 315 · 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 = 8 and x + 4y = 6 →
  2. 2.3x − 4y = −21 and 2x + 6y = 12 →
  3. 3.4x + 5y = 37 and 5x − y = 10 →
  4. 4.2x + 5y = 53 and 2x − 5y = −37 →
  5. 5.2x + 2y = 28 and x + 4y = 35 →
  6. 6.5x + y = 40 and x + 5y = −16 →
  7. 7.7x + 8y = 36 and 8x + 7y = 39 →
  8. 8.5x + 2y = 2 and 2x + 5y = 26 →
  9. 9.x + y = 1 and 2x + y = 3 →
  10. 10.6x − 3y = −81 and 2x − 5y = −63 →
  11. 11.5x − 5y = −10 and 6x + 2y = −20 →
  12. 12.6x + 6y = 18 and 3x − y = 13 →
  13. 13.3x + 3y = 27 and 4x + 6y = 46 →
  14. 14.3x − 2y = −5 and 6x + 6y = 60 →
  15. 15.5x + 5y = 55 and 3x + 5y = 51 →
  16. 16.2x − 4y = 6 and 4x − 5y = 15 →
  17. 17.9x + 6y = 81 and 6x + 9y = 69 →
  18. 18.6x + 3y = −33 and 3x + 6y = 15 →
  19. 19.x + 6y = 31 and 3x − y = 17 →
  20. 20.7x + 5y = −2 and 5x + 7y = 2 →
  21. 21.3x + y = −34 and 2x − 2y = −4 →
  22. 22.4x + 7y = −12 and 7x + 4y = 12 →
  23. 23.4x − 3y = 16 and 2x + y = 18 →
  24. 24.4x + y = 24 and x + 4y = 36 →
  25. 25.x − 2y = −14 and x − 6y = −30 →
  26. 26.2x + 2y = −8 and 4x − y = −6 →
  27. 27.7x + 6y = 56 and 6x + 7y = 61 →
  28. 28.8x + 5y = 26 and 5x + 8y = 26 →
  29. 29.6x − 6y = −30 and x + 6y = 37 →
  30. 30.4x + y = 2 and x + 4y = −22 →
  31. 31.6x + 7y = 61 and 7x + 6y = 69 →
  32. 32.x − 4y = −20 and 3x + 3y = 45 →
  33. 33.3x + 5y = 29 and 5x + 3y = 43 →
  34. 34.3x + 7y = 59 and 7x + 3y = 71 →
  35. 35.3x + 3y = 9 and 4x − 5y = 57 →
  36. 36.4x + y = 20 and 2x + 4y = 38 →
  37. 37.6x − 4y = −58 and x − 5y = −14 →
  38. 38.8x + y = 4 and x + 8y = −31 →
  39. 39.x + 3y = 25 and 3x + y = 19 →
  40. 40.6x + 3y = −36 and 4x + 6y = −8 →

Answer key

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

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