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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 590 · 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. 1.4x − 2y = 26 and x + y = −1 →
  2. 2.4x + 9y = 11 and 9x + 4y = 41 →
  3. 3.3x + y = 17 and 2x + 3y = 16 →
  4. 4.2x − 3y = 11 and 4x − 3y = 19 →
  5. 5.9x + 2y = −70 and 2x + 9y = −7 →
  6. 6.6x + 9y = 27 and 9x + 6y = 48 →
  7. 7.4x + 2y = −10 and 2x − 5y = −11 →
  8. 8.6x + 5y = 65 and 5x + 6y = 67 →
  9. 9.3x + 5y = −16 and 2x + 3y = −8 →
  10. 10.3x + 5y = −3 and 6x − 5y = 39 →
  11. 11.6x + 3y = −39 and x − 4y = −2 →
  12. 12.5x + y = −3 and 3x − 6y = −48 →
  13. 13.3x + 2y = 7 and 5x + 2y = 5 →
  14. 14.x + 6y = 59 and 4x + 6y = 74 →
  15. 15.5x − 6y = −35 and 5x + 2y = 5 →
  16. 16.3x + 4y = 43 and 4x + 5y = 55 →
  17. 17.8x + 5y = 4 and 5x + 8y = 22 →
  18. 18.3x + 2y = 29 and 5x + 6y = 67 →
  19. 19.2x + 8y = −76 and 8x + 2y = −64 →
  20. 20.x − y = 0 and 5x + 6y = 77 →
  21. 21.3x − 4y = −33 and 2x + 4y = 38 →
  22. 22.2x + 4y = 24 and 2x + 2y = 20 →
  23. 23.2x + 7y = −10 and 7x + 2y = 10 →
  24. 24.3x + 2y = 6 and 2x + 3y = 19 →
  25. 25.x + 2y = 27 and x + 5y = 54 →
  26. 26.4x − 6y = 72 and 6x − 4y = 68 →
  27. 27.4x − 3y = 20 and x + 3y = 20 →
  28. 28.4x + 5y = 36 and x + y = 7 →
  29. 29.x + y = 6 and x + 2y = 4 →
  30. 30.2x + y = 25 and 3x + y = 33 →
  31. 31.4x + 3y = 24 and 2x − y = 2 →
  32. 32.2x + 5y = −40 and 3x + 2y = −27 →
  33. 33.2x − 2y = 24 and 4x − 6y = 60 →
  34. 34.4x − y = −33 and x − 3y = −22 →
  35. 35.2x + 3y = −6 and 2x + y = 10 →
  36. 36.4x + 3y = −43 and x + 5y = −32 →
  37. 37.x + 4y = 15 and 4x + y = 15 →
  38. 38.3x + 5y = −36 and 5x + 4y = −34 →
  39. 39.4x − 3y = 30 and x + 6y = −6 →
  40. 40.3x + 3y = 33 and x + 2y = 20 →

Answer key

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

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