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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 333 · 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 − y = −31 and x − 4y = 11 →
  2. 2.5x − y = 24 and 6x + y = 9 →
  3. 3.5x + y = 40 and 2x − 5y = 43 →
  4. 4.2x − 4y = −18 and x − 3y = −15 →
  5. 5.5x − 6y = 19 and 5x − 4y = 21 →
  6. 6.7x + y = −13 and x + 7y = −43 →
  7. 7.7x + 9y = −17 and 9x + 7y = −31 →
  8. 8.3x − 2y = 20 and 3x + 3y = 30 →
  9. 9.2x + 6y = 0 and 4x + 3y = 27 →
  10. 10.3x + 6y = −6 and 3x + 5y = −7 →
  11. 11.x − 5y = −21 and 6x − 5y = 24 →
  12. 12.4x − 5y = 37 and 6x − 3y = 15 →
  13. 13.6x + 5y = −18 and 4x + 6y = 4 →
  14. 14.3x − y = −18 and 5x + 4y = 21 →
  15. 15.x + 5y = 49 and 5x + y = 53 →
  16. 16.5x − 5y = 15 and 3x + y = 25 →
  17. 17.7x + 8y = 93 and 8x + 7y = 87 →
  18. 18.3x − 4y = −15 and 4x + 2y = 46 →
  19. 19.6x − y = 10 and x + 4y = 35 →
  20. 20.6x + y = 37 and 2x − 6y = −32 →
  21. 21.8x + y = 39 and x + 8y = 60 →
  22. 22.6x + 5y = 28 and 5x + 3y = 21 →
  23. 23.6x + 2y = 34 and 4x − 2y = 36 →
  24. 24.x + 2y = −10 and 2x − 2y = 28 →
  25. 25.6x + 6y = 54 and x + 4y = 24 →
  26. 26.x + 6y = 53 and 6x + 5y = 70 →
  27. 27.9x + 5y = 69 and 5x + 9y = 57 →
  28. 28.6x + 5y = 52 and 5x + 6y = 47 →
  29. 29.x + 5y = −12 and x − 2y = 2 →
  30. 30.5x + 4y = 67 and 5x + 5y = 75 →
  31. 31.4x + 2y = 22 and 2x + 6y = 26 →
  32. 32.8x + 7y = −25 and 7x + 8y = −35 →
  33. 33.8x + 3y = 45 and 3x + 8y = 65 →
  34. 34.x + 7y = 50 and 7x + y = 14 →
  35. 35.2x + 6y = 8 and 6x + 2y = −40 →
  36. 36.9x + 2y = 40 and 2x + 9y = 26 →
  37. 37.5x + 5y = 30 and 2x + 5y = 33 →
  38. 38.2x + 4y = 20 and 2x − y = 0 →
  39. 39.2x − 2y = 0 and 4x + y = 15 →
  40. 40.3x + 2y = 14 and 2x + 3y = 11 →

Answer key

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

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