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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 320 · 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. 1.4x + 3y = −18 and 3x + 4y = −10 →
  2. 2.5x − y = 22 and 2x + 2y = 16 →
  3. 3.x + 6y = 29 and 6x + y = 34 →
  4. 4.4x + 4y = 20 and 5x + 6y = 24 →
  5. 5.6x + 2y = 38 and 6x − y = 17 →
  6. 6.4x + y = −44 and 4x − y = −28 →
  7. 7.2x + 5y = 34 and 5x + 6y = 59 →
  8. 8.6x − y = 4 and 3x + y = 14 →
  9. 9.x − 3y = −4 and 5x − 4y = 13 →
  10. 10.6x + 5y = −59 and 6x − 5y = −49 →
  11. 11.x − 5y = −33 and 4x + 4y = 36 →
  12. 12.3x + 6y = 21 and x − 6y = −9 →
  13. 13.2x + 5y = −29 and 2x − 6y = 48 →
  14. 14.4x − y = 33 and 6x + y = 27 →
  15. 15.6x + 4y = −48 and 2x + 6y = −30 →
  16. 16.6x − 3y = −21 and 5x + 5y = −70 →
  17. 17.3x − y = 13 and 2x + 2y = 30 →
  18. 18.2x − 2y = −24 and x + y = 4 →
  19. 19.4x − 4y = −8 and 5x + 2y = 18 →
  20. 20.4x + 6y = −28 and 6x + 4y = −32 →
  21. 21.3x + 7y = −81 and 7x + 3y = −69 →
  22. 22.4x + 5y = 71 and 6x − 6y = 12 →
  23. 23.4x − 4y = 4 and x + 3y = 13 →
  24. 24.2x + 5y = 1 and x + 2y = 2 →
  25. 25.2x + 5y = 59 and x − 5y = −38 →
  26. 26.3x + 8y = 25 and 8x + 3y = 30 →
  27. 27.2x + 7y = −56 and 7x + 2y = −61 →
  28. 28.6x + 3y = −9 and 3x + 4y = 3 →
  29. 29.2x + 6y = 28 and 6x − 2y = −56 →
  30. 30.x + 2y = 6 and 6x − 3y = −24 →
  31. 31.7x + y = 42 and x + 7y = 54 →
  32. 32.2x + 9y = −30 and 9x + 2y = 19 →
  33. 33.4x + 5y = −69 and 4x + 6y = −78 →
  34. 34.5x + 5y = 45 and 3x − 5y = −37 →
  35. 35.5x + 2y = 25 and 5x − y = 10 →
  36. 36.3x + 6y = 75 and 6x + 2y = 60 →
  37. 37.x − 4y = −1 and 5x − 3y = 29 →
  38. 38.3x + 6y = 0 and 6x + 3y = −18 →
  39. 39.3x + 2y = −20 and 4x − y = −34 →
  40. 40.x + y = 9 and 3x + 6y = 39 →

Answer key

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

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