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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 749 · 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 = 10 and 3x + 5y = −23 →
  2. 2.x + y = 7 and 5x + 2y = 20 →
  3. 3.2x + 2y = 8 and 6x + 4y = 30 →
  4. 4.6x + 3y = −9 and 5x + 3y = −3 →
  5. 5.4x + y = −21 and 6x + 6y = 0 →
  6. 6.6x + 3y = 27 and 5x + 5y = 5 →
  7. 7.9x + 8y = −71 and 8x + 9y = −65 →
  8. 8.4x + 3y = 14 and 3x + 4y = 7 →
  9. 9.6x + 2y = 8 and 4x − 2y = 2 →
  10. 10.2x + 5y = 27 and x + 4y = 24 →
  11. 11.x + 2y = 10 and 2x + y = 8 →
  12. 12.2x + 5y = −53 and 2x − 2y = −4 →
  13. 13.3x + 5y = 67 and 4x + 4y = 68 →
  14. 14.7x + 8y = 15 and 8x + 7y = 15 →
  15. 15.2x − y = 0 and 2x − 2y = 2 →
  16. 16.4x + 4y = 12 and 4x + 2y = −4 →
  17. 17.4x + 3y = −28 and x − 2y = 15 →
  18. 18.4x − 3y = 15 and x + 4y = 18 →
  19. 19.4x + 8y = 60 and 8x + 4y = 36 →
  20. 20.4x + 2y = −50 and 2x + 4y = −52 →
  21. 21.6x + y = 50 and x − y = −1 →
  22. 22.6x − 3y = 30 and 6x + 3y = 6 →
  23. 23.8x + 2y = 76 and 2x + 8y = 34 →
  24. 24.4x + 3y = 35 and 4x + y = 25 →
  25. 25.x − 2y = 8 and 3x + y = −25 →
  26. 26.2x − y = 13 and x + 6y = 0 →
  27. 27.2x + y = −13 and x + 2y = −11 →
  28. 28.x − 2y = 8 and 4x + 2y = 22 →
  29. 29.2x − y = −13 and 2x − 2y = −20 →
  30. 30.5x + 3y = −30 and 3x + 3y = −12 →
  31. 31.4x + 3y = 25 and 6x + 4y = 34 →
  32. 32.4x + 2y = 2 and 2x + 4y = 22 →
  33. 33.6x + 5y = 20 and 4x + 4y = 12 →
  34. 34.5x − 2y = 20 and 5x + 6y = 60 →
  35. 35.3x + 4y = 39 and 4x + 3y = 38 →
  36. 36.9x + 7y = 38 and 7x + 9y = 58 →
  37. 37.6x + 3y = 42 and 3x + 6y = 48 →
  38. 38.x + 2y = 0 and 2x + y = 9 →
  39. 39.5x + 5y = 0 and 2x + 5y = 6 →
  40. 40.2x + 4y = −20 and 4x + 2y = −28 →

Answer key

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

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