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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 657 · 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. 1.5x + 2y = −5 and 6x − 4y = 26 →
  2. 2.4x + 9y = 30 and 9x + 4y = 35 →
  3. 3.8x + 3y = 32 and 3x + 8y = 67 →
  4. 4.8x + 5y = 11 and 5x + 8y = 2 →
  5. 5.5x + 3y = 33 and 4x − 2y = 0 →
  6. 6.3x + 3y = 30 and 6x + 2y = 52 →
  7. 7.6x + y = 29 and x + 6y = 34 →
  8. 8.5x + 4y = 39 and 5x + 6y = 41 →
  9. 9.4x − 5y = −3 and 4x − 3y = −5 →
  10. 10.5x − 2y = 11 and 6x + 3y = 24 →
  11. 11.5x + y = 37 and x + 3y = 13 →
  12. 12.2x − 2y = −30 and 3x + 2y = −10 →
  13. 13.x − 3y = −26 and 6x + 6y = 36 →
  14. 14.2x + 5y = −34 and x + 4y = −29 →
  15. 15.6x + 5y = 33 and 5x + 6y = 33 →
  16. 16.2x + y = 14 and x + 2y = 19 →
  17. 17.6x + 4y = 78 and 6x − y = 48 →
  18. 18.4x + 6y = −30 and 6x + 4y = −50 →
  19. 19.3x − 3y = −42 and 2x + y = −13 →
  20. 20.4x + y = 31 and 3x − y = 25 →
  21. 21.2x + 4y = −10 and 4x + 3y = −25 →
  22. 22.4x + 9y = 17 and 9x + 4y = −43 →
  23. 23.x + y = 12 and 6x + 3y = 48 →
  24. 24.4x + 3y = −30 and 3x − 6y = −6 →
  25. 25.x − 2y = −10 and x − 4y = −22 →
  26. 26.4x + y = −6 and 2x + y = −2 →
  27. 27.x − y = 8 and 2x + y = 10 →
  28. 28.2x + 4y = −12 and 4x + 2y = 0 →
  29. 29.6x + 4y = 4 and 4x + 6y = −4 →
  30. 30.6x + 2y = −12 and 6x + y = −18 →
  31. 31.8x + 9y = 48 and 9x + 8y = 37 →
  32. 32.4x + 2y = −10 and 3x + 3y = −3 →
  33. 33.x + 6y = 50 and 3x − y = −2 →
  34. 34.2x + 4y = −4 and 4x + 2y = 22 →
  35. 35.x − y = 7 and 6x − y = 47 →
  36. 36.2x − 5y = −23 and 4x + y = 9 →
  37. 37.x − 6y = −8 and 4x + 2y = 20 →
  38. 38.7x + 2y = 66 and 2x + 7y = 51 →
  39. 39.6x − y = 8 and 2x − 2y = −4 →
  40. 40.3x + 2y = −28 and 2x + 3y = −22 →

Answer key

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

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