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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 620 · 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 + 3y = −25 and 2x − y = −13 →
  2. 2.4x − 6y = 12 and 3x + 3y = 39 →
  3. 3.2x + 6y = 10 and 6x + 2y = 14 →
  4. 4.3x − 5y = −29 and 6x − 3y = −30 →
  5. 5.3x + 2y = −13 and 4x + 3y = −16 →
  6. 6.2x + 3y = 18 and 3x + 2y = 17 →
  7. 7.7x + 2y = −53 and 2x + 7y = −28 →
  8. 8.3x + 2y = 13 and 6x − 6y = 6 →
  9. 9.7x + 2y = −13 and 2x + 7y = 22 →
  10. 10.x + 8y = 69 and 8x + y = 48 →
  11. 11.4x − y = 33 and x + 4y = −30 →
  12. 12.2x + 6y = 30 and 6x + 4y = 6 →
  13. 13.2x − y = 6 and x + 5y = 47 →
  14. 14.x − 6y = 47 and 5x + 6y = −89 →
  15. 15.4x − y = 12 and x − 2y = −4 →
  16. 16.x + 3y = −9 and 4x + 6y = −12 →
  17. 17.x + 6y = 13 and 2x + y = 4 →
  18. 18.6x − 5y = 51 and 6x + 3y = −21 →
  19. 19.2x + 4y = −30 and 4x + 2y = −36 →
  20. 20.x + y = −6 and 6x + 3y = −15 →
  21. 21.x − 3y = 9 and 6x + 4y = 32 →
  22. 22.3x + 6y = 63 and 5x + 6y = 73 →
  23. 23.3x + y = −26 and x + 3y = −30 →
  24. 24.2x + 2y = −16 and 6x − 2y = 24 →
  25. 25.5x + 3y = 40 and 3x + 5y = 40 →
  26. 26.4x + y = 7 and 3x − 2y = −3 →
  27. 27.x + 6y = 47 and 5x + 4y = 53 →
  28. 28.x + y = 6 and 4x + 6y = 26 →
  29. 29.5x + 6y = 23 and x + 4y = 13 →
  30. 30.8x + 5y = 5 and 5x + 8y = −31 →
  31. 31.5x − 4y = 71 and 3x + 2y = 3 →
  32. 32.2x + y = −2 and 4x + 3y = 2 →
  33. 33.5x + y = −22 and 6x + y = −27 →
  34. 34.6x + 4y = 56 and 4x + y = 29 →
  35. 35.5x + 4y = 29 and 3x + 4y = 19 →
  36. 36.7x + 6y = 27 and 6x + 7y = 38 →
  37. 37.6x + 5y = 39 and 5x + 6y = 38 →
  38. 38.x − y = 8 and 2x + 2y = 0 →
  39. 39.3x + 4y = −2 and x − 5y = 12 →
  40. 40.3x + y = −19 and 6x + y = −31 →

Answer key

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

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