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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 474 · 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 − 3y = 9 and x + 2y = 7 →
  2. 2.x − 5y = −25 and 6x + 3y = 48 →
  3. 3.6x + 5y = −6 and 6x + 6y = −12 →
  4. 4.4x + 5y = −52 and 2x + 2y = −22 →
  5. 5.4x + 6y = 66 and 6x + 4y = 64 →
  6. 6.x + y = 10 and 4x + y = 31 →
  7. 7.7x + 5y = 3 and 5x + 7y = 9 →
  8. 8.5x + 6y = 57 and 6x + 2y = 32 →
  9. 9.6x + 2y = −10 and 6x + y = −11 →
  10. 10.4x − 2y = −18 and 2x + 4y = 16 →
  11. 11.x + 2y = 6 and 3x + 3y = 3 →
  12. 12.x + 8y = 20 and 8x + y = 34 →
  13. 13.4x + 6y = 26 and 6x + 4y = 4 →
  14. 14.3x + 6y = −21 and 2x + 5y = −22 →
  15. 15.3x + 5y = 31 and 2x − 2y = 10 →
  16. 16.4x − 3y = −9 and 4x + 4y = 40 →
  17. 17.5x − 6y = 49 and 4x − 5y = 40 →
  18. 18.x + 2y = 6 and x + y = 5 →
  19. 19.3x + 4y = −3 and 4x + 3y = −18 →
  20. 20.5x + 2y = 17 and 5x + 3y = 18 →
  21. 21.5x + 2y = 16 and 5x − 5y = −5 →
  22. 22.x + 6y = −13 and 3x + 6y = −27 →
  23. 23.2x + y = 0 and x + 2y = 12 →
  24. 24.6x + 4y = −22 and x + 2y = 7 →
  25. 25.x + 9y = 43 and 9x + y = 67 →
  26. 26.4x − 5y = −23 and 2x + 2y = 20 →
  27. 27.5x + y = −19 and 6x + 2y = −26 →
  28. 28.5x + y = 17 and x + 5y = 37 →
  29. 29.x − 4y = −1 and 6x − y = −52 →
  30. 30.8x + 7y = 105 and 7x + 8y = 105 →
  31. 31.4x + 9y = 46 and 9x + 4y = 71 →
  32. 32.2x + 5y = 53 and 4x + 5y = 71 →
  33. 33.2x + y = 19 and x + 4y = 20 →
  34. 34.4x + 3y = 11 and 3x + 3y = 6 →
  35. 35.2x + y = 9 and x + 6y = −1 →
  36. 36.6x + 3y = 9 and 5x − 6y = −69 →
  37. 37.x − 4y = 2 and 4x − 3y = −5 →
  38. 38.2x + 5y = 31 and 5x + 2y = 25 →
  39. 39.6x + 6y = 42 and 2x − 5y = −42 →
  40. 40.3x + 5y = −42 and 5x + 3y = −22 →

Answer key

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

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