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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 207 · 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. 1.8x + 6y = −54 and 6x + 8y = −30 →
  2. 2.2x + 6y = −50 and x − 5y = 47 →
  3. 3.3x − y = 14 and x − 2y = −7 →
  4. 4.6x − 2y = 38 and x − y = 1 →
  5. 5.x + 2y = 11 and 2x − 3y = −13 →
  6. 6.4x + 2y = 2 and 2x + 3y = 19 →
  7. 7.2x + 5y = 19 and 5x + 2y = 16 →
  8. 8.2x + 7y = 62 and 7x + 2y = 37 →
  9. 9.6x − 3y = −54 and 5x + 4y = −6 →
  10. 10.4x + 5y = 5 and 5x + 4y = −5 →
  11. 11.4x − y = −37 and x + 6y = −3 →
  12. 12.3x + 4y = −11 and 3x + y = −14 →
  13. 13.x + 2y = 1 and 2x − 4y = −14 →
  14. 14.6x + 3y = 30 and 3x + 6y = −21 →
  15. 15.5x + 4y = −25 and 4x + 5y = −11 →
  16. 16.4x + 2y = 6 and 5x − 3y = 2 →
  17. 17.6x + 9y = −129 and 9x + 6y = −126 →
  18. 18.2x + 6y = 14 and 5x + 2y = −17 →
  19. 19.4x + 4y = 24 and 5x + 6y = 38 →
  20. 20.x + 6y = 51 and x − 6y = −45 →
  21. 21.2x + y = −2 and 3x − 5y = 23 →
  22. 22.3x + 2y = 18 and 2x + 3y = 22 →
  23. 23.3x − y = 9 and 4x + 3y = 25 →
  24. 24.9x + 2y = 76 and 2x + 9y = 34 →
  25. 25.5x + 3y = 53 and 2x − 6y = −22 →
  26. 26.9x + 7y = −68 and 7x + 9y = −60 →
  27. 27.4x + 2y = −10 and 2x + 4y = −32 →
  28. 28.3x + 5y = 27 and 5x + 3y = 29 →
  29. 29.8x + 2y = −36 and 2x + 8y = 36 →
  30. 30.4x + y = 3 and x + 4y = −3 →
  31. 31.x + y = −1 and 3x − 2y = −18 →
  32. 32.4x − 4y = 28 and 3x − 2y = 22 →
  33. 33.4x + 4y = 24 and x − 4y = 21 →
  34. 34.x − 5y = 45 and 6x + 6y = −18 →
  35. 35.4x + 4y = −40 and 5x + y = −14 →
  36. 36.x − 5y = 9 and 3x − 3y = 3 →
  37. 37.4x − y = −24 and 6x + 4y = −14 →
  38. 38.6x + 4y = 16 and 6x + 2y = 14 →
  39. 39.3x + 6y = 75 and 4x + y = 37 →
  40. 40.3x + 2y = 15 and 6x − 5y = 57 →

Answer key

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

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