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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 230 · 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 + y = 9 and x + 2y = 6 →
  2. 2.x + 2y = 22 and 2x + y = 23 →
  3. 3.3x + 3y = −3 and 5x − 4y = 58 →
  4. 4.x + 6y = 51 and 6x − 6y = 12 →
  5. 5.3x − 2y = −18 and 3x + y = 0 →
  6. 6.4x + 9y = −89 and 9x + 4y = −54 →
  7. 7.6x + 4y = 24 and 2x + 5y = 19 →
  8. 8.9x + 5y = 21 and 5x + 9y = 49 →
  9. 9.x + 6y = −55 and 6x − 2y = 12 →
  10. 10.5x − 5y = 0 and 6x − 4y = 18 →
  11. 11.8x + 9y = 64 and 9x + 8y = 55 →
  12. 12.3x + 8y = 23 and 8x + 3y = 43 →
  13. 13.2x + 4y = 4 and 4x + 2y = −10 →
  14. 14.6x − 5y = 55 and 6x + 2y = 20 →
  15. 15.5x + 3y = −3 and 4x − 6y = −78 →
  16. 16.x + 7y = 5 and 7x + y = −13 →
  17. 17.8x + 9y = −70 and 9x + 8y = −66 →
  18. 18.6x + 7y = −19 and 7x + 6y = −33 →
  19. 19.x + 2y = 14 and 6x − 5y = −69 →
  20. 20.6x + 4y = 42 and 2x − y = 0 →
  21. 21.7x + 9y = 20 and 9x + 7y = 12 →
  22. 22.2x − y = 1 and 2x + 4y = 26 →
  23. 23.8x + 2y = 16 and 2x + 8y = −56 →
  24. 24.3x + 5y = −33 and x + 2y = −14 →
  25. 25.x − y = 16 and x + 2y = −5 →
  26. 26.2x + 6y = 20 and 6x + 2y = 12 →
  27. 27.x + 4y = 21 and 5x + 3y = 3 →
  28. 28.3x + 3y = −45 and 2x + 5y = −57 →
  29. 29.4x + y = 17 and 2x − 3y = 19 →
  30. 30.x + 5y = 17 and x − 6y = −16 →
  31. 31.2x + 8y = 50 and 8x + 2y = −40 →
  32. 32.5x + 6y = −15 and 6x + 5y = −7 →
  33. 33.6x − 4y = 52 and 2x − y = 15 →
  34. 34.7x + 4y = −23 and 4x + 7y = 1 →
  35. 35.2x + 4y = −18 and 3x − y = −6 →
  36. 36.3x + y = 29 and 5x + 5y = 55 →
  37. 37.8x + 6y = −46 and 6x + 8y = −24 →
  38. 38.2x + 5y = −29 and 5x + 2y = −41 →
  39. 39.4x + 2y = 30 and 3x − 6y = −30 →
  40. 40.3x + 8y = −33 and 8x + 3y = 22 →

Answer key

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

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