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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 701 · 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. 1.4x − y = 10 and 2x + 2y = 0 →
  2. 2.3x + 2y = −1 and 4x + 3y = −4 →
  3. 3.4x + 2y = 36 and 2x + 4y = 42 →
  4. 4.2x − 5y = 23 and 3x + 4y = 23 →
  5. 5.4x − 6y = −32 and 6x + 2y = 18 →
  6. 6.3x + 5y = 37 and 5x + y = 25 →
  7. 7.2x − 5y = 47 and 6x + 6y = −48 →
  8. 8.3x − 6y = −39 and 6x + 5y = 41 →
  9. 9.4x + 2y = −2 and 2x + 4y = 8 →
  10. 10.9x + 7y = 82 and 7x + 9y = 78 →
  11. 11.x + 5y = −28 and x + 3y = −16 →
  12. 12.x + 4y = −13 and 4x + y = −7 →
  13. 13.9x + 8y = 65 and 8x + 9y = 54 →
  14. 14.5x − y = −37 and 2x + 3y = −8 →
  15. 15.2x + 5y = 14 and 2x + y = −2 →
  16. 16.4x − 6y = −50 and 5x + 3y = 32 →
  17. 17.x + y = 14 and 2x + 6y = 52 →
  18. 18.2x + 4y = 22 and 4x + 2y = −4 →
  19. 19.2x + 3y = 12 and x − 2y = 13 →
  20. 20.x − y = −11 and 4x + 4y = −4 →
  21. 21.x + 8y = 59 and 8x + y = −32 →
  22. 22.3x + 6y = 33 and 2x + y = 16 →
  23. 23.6x + y = −10 and x + 6y = −25 →
  24. 24.7x + 4y = 51 and 4x + 7y = 15 →
  25. 25.6x + y = 61 and x − y = 2 →
  26. 26.9x + 7y = −51 and 7x + 9y = −61 →
  27. 27.3x − y = 25 and x + 2y = 13 →
  28. 28.2x + 3y = −2 and 3x + 5y = −2 →
  29. 29.4x − 5y = −27 and 4x + 5y = 43 →
  30. 30.4x + 3y = 38 and 3x + 4y = 39 →
  31. 31.4x + 5y = 15 and 5x + 4y = 3 →
  32. 32.8x + 2y = −10 and 2x + 8y = 20 →
  33. 33.3x − 2y = 7 and x − 2y = −3 →
  34. 34.7x + y = 43 and x + 7y = 61 →
  35. 35.3x + 7y = −6 and 7x + 3y = −54 →
  36. 36.5x + 3y = 8 and 3x + 5y = 8 →
  37. 37.5x + 6y = 44 and 4x + 2y = 24 →
  38. 38.5x + 3y = 34 and 3x + 5y = 30 →
  39. 39.6x − 6y = −30 and 6x + y = 26 →
  40. 40.7x + 3y = 28 and 3x + 7y = −28 →

Answer key

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

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