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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 561 · 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. 1.5x + y = 44 and x + 5y = 52 →
  2. 2.2x + 3y = 27 and 4x + 4y = 44 →
  3. 3.2x + 8y = −46 and 8x + 2y = 26 →
  4. 4.x + 8y = 33 and 8x + y = −51 →
  5. 5.5x + y = 23 and x − 6y = 48 →
  6. 6.2x + 3y = −12 and 4x + 2y = 0 →
  7. 7.2x + 8y = 40 and 8x + 2y = 40 →
  8. 8.x + y = 7 and 2x + y = 12 →
  9. 9.2x + y = 12 and 3x − y = 33 →
  10. 10.4x + 3y = −19 and 3x + 5y = −6 →
  11. 11.2x + 3y = −13 and x + y = −5 →
  12. 12.5x − 6y = 81 and 2x + 4y = −6 →
  13. 13.x + 3y = −9 and x − 4y = 5 →
  14. 14.3x + y = −3 and 5x + 4y = 16 →
  15. 15.5x + 2y = −17 and 2x + 5y = 31 →
  16. 16.x + y = 3 and 5x − 6y = 4 →
  17. 17.2x + 6y = 18 and 2x + y = −12 →
  18. 18.4x − 6y = −50 and 6x + 5y = 51 →
  19. 19.5x − 6y = −46 and x − 3y = −20 →
  20. 20.9x + 6y = 99 and 6x + 9y = 96 →
  21. 21.4x + 9y = −5 and 9x + 4y = 5 →
  22. 22.5x − 2y = −34 and x + 3y = 0 →
  23. 23.2x + y = −11 and x + 2y = 2 →
  24. 24.5x + 6y = 49 and 5x + y = 4 →
  25. 25.x + 9y = 48 and 9x + y = 32 →
  26. 26.6x + y = −2 and x + 4y = −31 →
  27. 27.x − y = −10 and 5x + 5y = 10 →
  28. 28.5x + 3y = 60 and 3x + 5y = 52 →
  29. 29.7x + 9y = −121 and 9x + 7y = −119 →
  30. 30.x − 4y = 11 and 2x − y = 1 →
  31. 31.8x + 5y = −14 and 5x + 8y = 1 →
  32. 32.4x + 3y = 22 and 5x − 5y = 10 →
  33. 33.x + 2y = 5 and 3x − 6y = 27 →
  34. 34.2x − 5y = 29 and x − 2y = 12 →
  35. 35.5x + y = 4 and 5x − 2y = 22 →
  36. 36.3x − 4y = 59 and 2x + 4y = −14 →
  37. 37.5x + 9y = −22 and 9x + 5y = −6 →
  38. 38.6x − y = 3 and 3x + y = 6 →
  39. 39.2x + 4y = −12 and 4x + 4y = 0 →
  40. 40.9x + y = 87 and x + 9y = 63 →

Answer key

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

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