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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 569 · 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 + 4y = 16 and 6x + 3y = 39 →
  2. 2.x + 4y = −11 and 6x + 5y = 10 →
  3. 3.4x + 2y = 20 and 2x + 4y = 28 →
  4. 4.5x + y = −18 and 5x + 5y = −10 →
  5. 5.4x + 5y = −22 and 5x + 4y = −23 →
  6. 6.2x + 2y = 0 and x − 5y = −12 →
  7. 7.x − 5y = −18 and 5x + y = −12 →
  8. 8.x + 5y = 36 and 5x + y = −36 →
  9. 9.x + 3y = −23 and 3x + y = −13 →
  10. 10.2x + 8y = −46 and 8x + 2y = 26 →
  11. 11.4x + 3y = −2 and 6x + y = 4 →
  12. 12.6x + y = 27 and x + 5y = 19 →
  13. 13.5x + 6y = 83 and 6x + 5y = 82 →
  14. 14.4x − 6y = −14 and 6x − 5y = −9 →
  15. 15.5x + 5y = −30 and 5x + 6y = −35 →
  16. 16.4x + 6y = 82 and 5x + 2y = 53 →
  17. 17.x + 5y = 39 and 2x − 5y = −42 →
  18. 18.5x + 4y = 22 and 2x + 4y = 16 →
  19. 19.6x + 9y = 18 and 9x + 6y = 57 →
  20. 20.5x − 4y = −1 and 3x − 2y = 3 →
  21. 21.4x + 3y = 14 and 5x − 4y = 2 →
  22. 22.3x + 5y = 2 and 5x + 3y = 14 →
  23. 23.x + 6y = −20 and 2x + 2y = −10 →
  24. 24.5x + 7y = −69 and 7x + 5y = −63 →
  25. 25.2x − 3y = 4 and 4x − 3y = 14 →
  26. 26.4x − 5y = −36 and 4x + 6y = 52 →
  27. 27.5x − 6y = −70 and x + 6y = 22 →
  28. 28.4x + 3y = −7 and 2x + 5y = 21 →
  29. 29.5x + 2y = −35 and 5x + 3y = −40 →
  30. 30.3x + y = 16 and x + 2y = 7 →
  31. 31.3x + 6y = 12 and x − 6y = −44 →
  32. 32.6x + 5y = 34 and x + 6y = 47 →
  33. 33.5x + 6y = 65 and 6x − y = 37 →
  34. 34.2x + y = 3 and 5x + 3y = 11 →
  35. 35.x + 4y = 5 and 4x + y = 35 →
  36. 36.2x + 2y = 8 and 4x + y = 19 →
  37. 37.3x − 5y = −32 and 4x + 4y = 0 →
  38. 38.9x + 5y = 12 and 5x + 9y = −12 →
  39. 39.3x − 2y = 2 and x + 4y = 38 →
  40. 40.x − y = −1 and x − 3y = 9 →

Answer key

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

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