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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 43 · 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 − 3y = 21 and 6x + 5y = 77 →
  2. 2.6x − 4y = 18 and 4x − y = 17 →
  3. 3.6x + 3y = −75 and 2x + 2y = −34 →
  4. 4.x + y = −12 and 3x − 4y = 27 →
  5. 5.6x + 3y = −33 and 2x + 6y = 4 →
  6. 6.3x + 2y = 14 and 2x + 3y = 11 →
  7. 7.6x + 3y = −27 and 2x + 4y = −18 →
  8. 8.5x + 9y = 116 and 9x + 5y = 108 →
  9. 9.x + 9y = 37 and 9x + y = 13 →
  10. 10.7x + 5y = −43 and 5x + 7y = −17 →
  11. 11.4x − 6y = −22 and x + 5y = 14 →
  12. 12.5x + 6y = 58 and 2x + 5y = 44 →
  13. 13.3x + 6y = 27 and 6x + 3y = 27 →
  14. 14.3x − 6y = 42 and 2x − y = 4 →
  15. 15.6x + 7y = −74 and 7x + 6y = −69 →
  16. 16.x + 6y = 39 and 2x + 4y = 30 →
  17. 17.x + 2y = 13 and x + 3y = 18 →
  18. 18.5x − 6y = 14 and 6x + y = 25 →
  19. 19.x + 2y = −2 and 2x + y = 11 →
  20. 20.x + 2y = 0 and 2x + y = −3 →
  21. 21.2x + y = 14 and x + 2y = 4 →
  22. 22.3x − 6y = −6 and 3x − 4y = 4 →
  23. 23.3x + 6y = 9 and 5x + 2y = 39 →
  24. 24.8x + 3y = 96 and 3x + 8y = 91 →
  25. 25.2x − 3y = −21 and 5x − y = 6 →
  26. 26.8x + 9y = −21 and 9x + 8y = −13 →
  27. 27.x + 4y = 39 and x + y = 15 →
  28. 28.4x − 5y = −67 and x + y = −1 →
  29. 29.5x + 4y = −3 and 5x + 5y = 0 →
  30. 30.3x + 4y = 41 and 4x + 3y = 36 →
  31. 31.5x + 3y = −8 and 3x + 4y = −7 →
  32. 32.x + 5y = −4 and 5x + y = 28 →
  33. 33.3x + 4y = 19 and 4x + 3y = 30 →
  34. 34.3x + 6y = −21 and 4x + y = 21 →
  35. 35.6x + 5y = 17 and x − y = 1 →
  36. 36.2x − 6y = 38 and 6x + 5y = −24 →
  37. 37.3x + 9y = 75 and 9x + 3y = 33 →
  38. 38.6x + y = 48 and x + 6y = 43 →
  39. 39.3x − y = 6 and x − 2y = 7 →
  40. 40.6x − 3y = 54 and 2x − 5y = 26 →

Answer key

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

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