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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 610 · 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 + 3y = −22 and 3x + 4y = −13 →
  2. 2.5x + y = 32 and x + 5y = 40 →
  3. 3.x − 5y = −15 and x − 6y = −19 →
  4. 4.6x − 5y = 33 and 3x + y = −15 →
  5. 5.5x + 4y = 17 and 6x + 4y = 22 →
  6. 6.6x + 4y = 62 and 6x + y = 47 →
  7. 7.2x + 6y = 32 and 4x + 6y = 40 →
  8. 8.6x + 2y = −2 and x + 5y = −33 →
  9. 9.6x − 2y = −10 and 3x + y = −7 →
  10. 10.x − 5y = −31 and x + 2y = 25 →
  11. 11.x + 5y = 32 and 5x + y = 40 →
  12. 12.5x + 2y = 53 and x − 3y = −3 →
  13. 13.7x + 3y = −25 and 3x + 7y = −5 →
  14. 14.8x + 3y = −17 and 3x + 8y = 28 →
  15. 15.4x + 6y = 26 and x + y = 2 →
  16. 16.2x + 4y = −4 and 5x + 3y = −17 →
  17. 17.x + 6y = 10 and 6x + y = 25 →
  18. 18.6x + y = 1 and 5x + 6y = 37 →
  19. 19.3x − 3y = 48 and 5x + 6y = −19 →
  20. 20.5x + 2y = 41 and 3x + y = 24 →
  21. 21.9x + 6y = −9 and 6x + 9y = 39 →
  22. 22.5x + 3y = 69 and 3x + 5y = 67 →
  23. 23.3x − 5y = 3 and x + 4y = 18 →
  24. 24.2x + y = 8 and x + 4y = 25 →
  25. 25.x + 2y = 6 and 3x + y = 8 →
  26. 26.4x + 9y = −66 and 9x + 4y = −51 →
  27. 27.9x + 3y = 21 and 3x + 9y = 15 →
  28. 28.3x + y = 14 and 2x + 6y = 20 →
  29. 29.6x + 4y = 80 and x − 4y = −24 →
  30. 30.2x + 2y = −2 and x + 3y = 13 →
  31. 31.6x + y = −33 and x + 6y = 47 →
  32. 32.3x + 8y = 50 and 8x + 3y = 60 →
  33. 33.7x + 2y = 72 and 2x + 7y = 72 →
  34. 34.4x − 6y = −38 and x + 2y = 1 →
  35. 35.2x + 5y = 24 and 2x + 2y = 12 →
  36. 36.5x + 3y = 7 and 2x − 3y = −14 →
  37. 37.6x + 5y = −3 and 2x + 5y = 9 →
  38. 38.7x + 2y = −1 and 2x + 7y = 19 →
  39. 39.4x + 3y = −22 and 3x + 4y = −13 →
  40. 40.2x + 6y = 20 and x − 5y = 2 →

Answer key

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

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