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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 703 · 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. 1.3x + y = 19 and 6x − 5y = 10 →
  2. 2.5x + 3y = 29 and 2x − 6y = −46 →
  3. 3.2x + 5y = 37 and 5x + 2y = 19 →
  4. 4.2x − 2y = −18 and 2x + 6y = 46 →
  5. 5.6x + 3y = −3 and x + 2y = −11 →
  6. 6.x + 4y = −17 and 4x + y = −8 →
  7. 7.2x + 2y = −6 and 3x + 4y = −13 →
  8. 8.x + 3y = −24 and 3x + y = 0 →
  9. 9.5x + 2y = −19 and 4x + 4y = −8 →
  10. 10.x − 4y = 0 and 6x + 4y = 56 →
  11. 11.9x + 3y = −24 and 3x + 9y = 24 →
  12. 12.x − 6y = −60 and 4x − 6y = −78 →
  13. 13.2x + 5y = 46 and 6x + 4y = 72 →
  14. 14.5x + 6y = −43 and x + 6y = −23 →
  15. 15.6x + 9y = 27 and 9x + 6y = −12 →
  16. 16.5x + 6y = 49 and 4x + y = 24 →
  17. 17.5x − 4y = −56 and 5x + y = −11 →
  18. 18.x + 5y = 4 and x − 4y = −5 →
  19. 19.2x + 5y = −29 and 3x + 5y = −31 →
  20. 20.6x + 5y = 28 and 5x + 6y = 27 →
  21. 21.2x + 3y = 5 and 6x + 3y = 9 →
  22. 22.2x + 3y = −10 and 6x + 4y = 0 →
  23. 23.x + 6y = 13 and 4x − 4y = −32 →
  24. 24.6x + y = −16 and 4x + 2y = −16 →
  25. 25.4x − y = 4 and 5x + 4y = 26 →
  26. 26.3x − 6y = 30 and 5x − 3y = 22 →
  27. 27.8x + 2y = −26 and 2x + 8y = 16 →
  28. 28.2x − 4y = −14 and 6x + 5y = 60 →
  29. 29.2x − 4y = −28 and 6x + 4y = −4 →
  30. 30.4x + 3y = 27 and 5x + y = 20 →
  31. 31.2x + 4y = 46 and 2x + y = 25 →
  32. 32.x − 3y = 6 and 4x − 4y = 32 →
  33. 33.2x − y = 6 and x + y = 12 →
  34. 34.x − 2y = −2 and x + y = 7 →
  35. 35.2x + 6y = −42 and 4x + 2y = −24 →
  36. 36.3x − y = 23 and 4x + 4y = 20 →
  37. 37.2x + y = −17 and x − 2y = −11 →
  38. 38.x + 4y = 10 and 5x + 4y = 18 →
  39. 39.4x + 8y = 76 and 8x + 4y = 68 →
  40. 40.3x + 4y = 16 and 4x + 3y = 5 →

Answer key

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

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