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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 726 · 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 + 6y = 9 and 4x + y = −16 →
  2. 2.3x + 6y = 69 and 4x − 3y = −7 →
  3. 3.4x + y = 37 and 2x − 2y = −4 →
  4. 4.2x − 6y = 6 and 2x + 6y = 18 →
  5. 5.3x − 2y = 39 and 6x + 6y = 18 →
  6. 6.4x + 2y = 46 and 2x + 4y = 38 →
  7. 7.6x + y = 31 and 5x + 3y = 41 →
  8. 8.7x + 8y = 11 and 8x + 7y = 4 →
  9. 9.7x + y = 6 and x + 7y = −6 →
  10. 10.4x + y = 24 and x − 2y = 24 →
  11. 11.2x + 2y = 22 and x − y = −7 →
  12. 12.3x + 2y = −6 and 2x − y = 17 →
  13. 13.3x + 4y = −11 and x + 2y = −7 →
  14. 14.2x + 2y = 18 and 5x − 4y = 0 →
  15. 15.8x + y = 29 and x + 8y = 43 →
  16. 16.5x − 3y = 21 and 4x − 2y = 18 →
  17. 17.2x + 4y = 26 and 5x + 6y = 37 →
  18. 18.6x + 5y = 51 and 5x + 6y = 59 →
  19. 19.x − 2y = −1 and 6x − 4y = 2 →
  20. 20.6x + 4y = −8 and 2x + 5y = −21 →
  21. 21.2x − 5y = 33 and x + 3y = 0 →
  22. 22.3x + y = −8 and x + 3y = 8 →
  23. 23.4x − 6y = 24 and 2x − 4y = 10 →
  24. 24.x − 6y = −2 and 4x − 5y = 11 →
  25. 25.5x + 4y = 56 and 3x − 6y = −42 →
  26. 26.2x + 5y = 31 and 5x + 2y = 46 →
  27. 27.3x + 5y = 21 and 5x + 6y = 28 →
  28. 28.x + 5y = 43 and 5x − 6y = −33 →
  29. 29.4x + 6y = −28 and 6x + 4y = −12 →
  30. 30.6x − 6y = −60 and 4x + 4y = −16 →
  31. 31.4x + 8y = −44 and 8x + 4y = 8 →
  32. 32.x − 4y = −42 and 4x + 6y = 30 →
  33. 33.4x + 2y = 14 and 3x + 3y = 3 →
  34. 34.3x + 9y = 105 and 9x + 3y = 99 →
  35. 35.9x + 8y = −5 and 8x + 9y = 5 →
  36. 36.4x + y = 29 and x + 4y = 41 →
  37. 37.6x + 2y = 42 and 2x + 6y = 30 →
  38. 38.2x + y = 15 and 2x + 3y = 21 →
  39. 39.6x + 2y = 40 and 2x + 6y = 24 →
  40. 40.6x + 6y = −18 and 6x + 5y = −23 →

Answer key

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

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