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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 574 · 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. 1.3x + y = −7 and 5x + 6y = 10 →
  2. 2.2x − y = −18 and 3x + 3y = −9 →
  3. 3.x + 4y = 14 and 6x + y = 15 →
  4. 4.5x − 2y = −9 and 2x + y = 0 →
  5. 5.2x − 2y = −8 and 4x + 6y = −6 →
  6. 6.6x + 7y = 28 and 7x + 6y = 37 →
  7. 7.x + 3y = 25 and 3x + y = 27 →
  8. 8.5x + y = −28 and 5x + 3y = −14 →
  9. 9.6x + 5y = 69 and 3x + y = 30 →
  10. 10.x + 6y = 56 and 5x + 6y = 88 →
  11. 11.5x − 2y = 23 and x + 2y = 7 →
  12. 12.7x + 3y = 53 and 3x + 7y = 57 →
  13. 13.4x + 6y = 70 and 6x + 4y = 70 →
  14. 14.x − 2y = −10 and 4x − 2y = 2 →
  15. 15.3x + 6y = 0 and 3x + 2y = 4 →
  16. 16.6x + y = −35 and x + 6y = 0 →
  17. 17.x + 2y = 18 and 2x − 6y = −34 →
  18. 18.x − y = 2 and 3x + 2y = 21 →
  19. 19.2x + 3y = 4 and 3x + 2y = −4 →
  20. 20.4x − 2y = −4 and 3x + 4y = 41 →
  21. 21.7x + 6y = −22 and 6x + 7y = −30 →
  22. 22.4x − y = −24 and 2x + 2y = 8 →
  23. 23.5x + y = −35 and 3x − 4y = −44 →
  24. 24.3x − y = −5 and x + 2y = 3 →
  25. 25.5x − y = 0 and 4x − 3y = −11 →
  26. 26.4x − 6y = 0 and x − 6y = −9 →
  27. 27.3x + y = 15 and x + 2y = 0 →
  28. 28.7x + 6y = 25 and 6x + 7y = 27 →
  29. 29.6x + 2y = 14 and 2x + 6y = 26 →
  30. 30.3x + 4y = 20 and 6x + 6y = 36 →
  31. 31.3x + 2y = 28 and x + 3y = 28 →
  32. 32.3x − y = −5 and 6x − 4y = −26 →
  33. 33.5x + 2y = −30 and 6x − 5y = −73 →
  34. 34.2x + 5y = 50 and 5x + 2y = 41 →
  35. 35.4x + 2y = 44 and 6x + y = 58 →
  36. 36.2x + 6y = −62 and 4x + 5y = −61 →
  37. 37.3x − 5y = −11 and 6x + 5y = −7 →
  38. 38.2x + 2y = −16 and 3x + 6y = −51 →
  39. 39.4x + 2y = −14 and x + 4y = −21 →
  40. 40.8x + 5y = 76 and 5x + 8y = 67 →

Answer key

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

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