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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 948 · 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 − 2y = 46 and 2x + 4y = −8 →
  2. 2.4x + 6y = 6 and 2x + 2y = 4 →
  3. 3.x − 4y = 12 and 6x + 3y = 45 →
  4. 4.7x + 4y = 83 and 4x + 7y = 71 →
  5. 5.x + 2y = −11 and 2x + y = −7 →
  6. 6.2x + 5y = 31 and 4x + 3y = −1 →
  7. 7.x + 2y = −18 and 2x + y = −18 →
  8. 8.2x − 3y = −3 and 3x − y = 6 →
  9. 9.2x − 4y = 32 and 6x − 3y = 60 →
  10. 10.5x + 3y = 26 and 3x + 5y = 38 →
  11. 11.2x + 6y = −20 and 6x + 6y = −12 →
  12. 12.6x + y = 15 and x + 2y = −3 →
  13. 13.3x + 4y = −30 and 2x − 3y = 14 →
  14. 14.4x + 6y = −28 and 4x + 3y = −4 →
  15. 15.7x + 3y = 72 and 3x + 7y = 48 →
  16. 16.2x + y = −3 and 5x + 3y = −6 →
  17. 17.5x + 2y = 19 and 3x + y = 11 →
  18. 18.4x − 4y = 12 and x + 4y = 18 →
  19. 19.5x + y = 14 and 6x + 6y = 60 →
  20. 20.5x + 2y = 21 and 6x + 6y = 36 →
  21. 21.x + 7y = 37 and 7x + y = 19 →
  22. 22.2x + 3y = 30 and 2x + 2y = 24 →
  23. 23.x + y = 15 and 2x − 3y = −15 →
  24. 24.3x + y = −16 and x + 3y = −8 →
  25. 25.5x + 5y = 20 and x − y = −14 →
  26. 26.2x + 3y = 5 and 3x + 2y = −5 →
  27. 27.x + 5y = 53 and 4x − 2y = 14 →
  28. 28.6x − 4y = 8 and 3x − y = −1 →
  29. 29.6x + y = 0 and 5x − y = −11 →
  30. 30.2x + 5y = 11 and x + 4y = 4 →
  31. 31.2x + 3y = −38 and x + 6y = −55 →
  32. 32.5x + 6y = 25 and x + 2y = 9 →
  33. 33.x + 4y = 6 and 5x + 4y = −18 →
  34. 34.x + 6y = 27 and 2x − 4y = −42 →
  35. 35.3x − y = 5 and 6x + y = −14 →
  36. 36.4x + 4y = −4 and x − 2y = 8 →
  37. 37.5x − 3y = −54 and x − 6y = −27 →
  38. 38.4x + 4y = −4 and x − 3y = 15 →
  39. 39.9x + 7y = 16 and 7x + 9y = 16 →
  40. 40.3x + 6y = 0 and 6x + 2y = −10 →

Answer key

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

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