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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 448 · 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. 1.6x + y = 19 and x + 6y = 9 →
  2. 2.5x + 2y = −7 and 4x − 3y = 22 →
  3. 3.x + 3y = 24 and 3x + 5y = 52 →
  4. 4.2x + 2y = 12 and x + 3y = 10 →
  5. 5.x + 4y = 37 and x + 6y = 55 →
  6. 6.4x + 2y = 0 and 2x − y = 12 →
  7. 7.5x + 3y = 4 and x + 4y = −6 →
  8. 8.4x + 7y = 45 and 7x + 4y = 54 →
  9. 9.5x + 3y = 43 and x + 4y = 29 →
  10. 10.2x − y = −1 and 5x − 5y = −20 →
  11. 11.4x + y = 21 and 2x + 6y = 16 →
  12. 12.6x + 3y = 54 and x + y = 11 →
  13. 13.5x + 5y = 0 and 6x + 2y = −20 →
  14. 14.x + 5y = −23 and 5x + y = −43 →
  15. 15.6x + 7y = 74 and 7x + 6y = 69 →
  16. 16.x + 8y = 25 and 8x + y = 11 →
  17. 17.2x + 3y = 0 and 4x + 2y = 16 →
  18. 18.4x − 2y = 52 and 5x + 6y = −3 →
  19. 19.9x + 6y = 66 and 6x + 9y = 84 →
  20. 20.2x + 4y = 2 and 4x + 2y = −8 →
  21. 21.2x + 4y = −28 and 4x + 2y = −38 →
  22. 22.x − 6y = −11 and 4x + 3y = 37 →
  23. 23.6x + 2y = 60 and 2x + 6y = 68 →
  24. 24.4x + y = 32 and 3x − 6y = −30 →
  25. 25.4x + 3y = 38 and 6x + 3y = 54 →
  26. 26.2x + 7y = 25 and 7x + 2y = −25 →
  27. 27.x + 8y = 57 and 8x + y = 15 →
  28. 28.x − 2y = 25 and x + 3y = −15 →
  29. 29.5x − y = 26 and 5x + 3y = 22 →
  30. 30.5x + 7y = 68 and 7x + 5y = 76 →
  31. 31.9x + 2y = 49 and 2x + 9y = 28 →
  32. 32.6x + 9y = 84 and 9x + 6y = 96 →
  33. 33.5x + y = 13 and x + 5y = 41 →
  34. 34.4x + 3y = −18 and 4x − y = −42 →
  35. 35.4x + y = 10 and 2x + 6y = 16 →
  36. 36.2x − 5y = −39 and 4x + 3y = 39 →
  37. 37.8x + 2y = 34 and 2x + 8y = 46 →
  38. 38.x + 2y = 18 and 2x + y = 15 →
  39. 39.6x − 6y = 36 and 2x + 5y = −37 →
  40. 40.6x + 5y = 58 and 5x + 6y = 63 →

Answer key

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

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