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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 138 · 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. 1.9x + 7y = 32 and 7x + 9y = 0 →
  2. 2.x − 4y = −10 and 6x + y = −35 →
  3. 3.5x + 4y = 18 and 6x − y = 10 →
  4. 4.5x + 8y = 0 and 8x + 5y = 39 →
  5. 5.4x + y = 30 and x + 4y = 15 →
  6. 6.2x + 2y = −28 and 6x − 5y = −18 →
  7. 7.9x + 2y = 74 and 2x + 9y = 25 →
  8. 8.3x + 5y = 23 and 2x + 6y = 18 →
  9. 9.4x + 5y = 14 and 3x − 2y = −24 →
  10. 10.x − y = −7 and 4x + 5y = 26 →
  11. 11.5x + 9y = 79 and 9x + 5y = 75 →
  12. 12.6x + 4y = −30 and 5x + 2y = −13 →
  13. 13.2x + 4y = 6 and 5x + 6y = −9 →
  14. 14.6x + y = 19 and 3x − y = −1 →
  15. 15.2x + 5y = 8 and x + y = −2 →
  16. 16.3x + 6y = 57 and 6x + 3y = 33 →
  17. 17.2x + y = 10 and 2x + 3y = 14 →
  18. 18.5x + 6y = 84 and 4x + 4y = 60 →
  19. 19.6x + 2y = 0 and x + 2y = 10 →
  20. 20.4x + 3y = 12 and 3x + 4y = 23 →
  21. 21.6x + 2y = 40 and 2x + 2y = 16 →
  22. 22.5x + 2y = 30 and x + 6y = 34 →
  23. 23.2x − 2y = 4 and x + 2y = −1 →
  24. 24.2x − 6y = 46 and 5x + 4y = 20 →
  25. 25.5x + 4y = 48 and 6x + 6y = 60 →
  26. 26.x + 4y = 15 and 3x − 6y = −9 →
  27. 27.5x + 6y = 27 and 4x − 2y = 8 →
  28. 28.8x + 4y = 4 and 4x + 8y = 20 →
  29. 29.4x + 6y = 74 and 5x + 6y = 82 →
  30. 30.7x + 5y = 18 and 5x + 7y = −18 →
  31. 31.4x − 6y = −52 and 2x + 6y = 28 →
  32. 32.5x − 6y = −3 and 2x − 6y = −30 →
  33. 33.x + 6y = 21 and 6x − 5y = 44 →
  34. 34.2x + y = 3 and x + 2y = 3 →
  35. 35.x − y = 9 and 3x + 6y = −36 →
  36. 36.6x − 3y = −63 and 6x + 5y = −39 →
  37. 37.2x + 4y = 38 and 6x + 6y = 78 →
  38. 38.3x + 2y = 31 and 2x + 3y = 24 →
  39. 39.5x + 8y = 58 and 8x + 5y = 46 →
  40. 40.2x − 3y = −16 and 2x − 6y = −40 →

Answer key

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

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