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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 642 · 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 + 6y = −30 and 2x − 4y = 52 →
  2. 2.x + 2y = 7 and 2x + y = 8 →
  3. 3.4x − 5y = 72 and 5x − y = 48 →
  4. 4.3x + y = 9 and 2x − y = −4 →
  5. 5.6x + 6y = 0 and x + 6y = 5 →
  6. 6.x + 5y = 7 and 3x + 3y = 9 →
  7. 7.5x + 7y = 19 and 7x + 5y = 17 →
  8. 8.4x + 2y = −14 and 5x − 4y = −76 →
  9. 9.2x − 6y = −52 and 2x + 2y = 12 →
  10. 10.3x + y = 31 and 4x + 5y = 56 →
  11. 11.x + y = −3 and 6x + 5y = −10 →
  12. 12.2x + y = 14 and 5x + 6y = 49 →
  13. 13.2x + 6y = −6 and 5x + 6y = −33 →
  14. 14.x + 5y = −53 and 5x + y = −49 →
  15. 15.3x − y = 17 and x − y = 1 →
  16. 16.5x + 4y = −19 and x − 4y = −23 →
  17. 17.7x + 3y = 16 and 3x + 7y = 24 →
  18. 18.2x + 5y = 19 and 5x + 3y = 19 →
  19. 19.5x + y = −27 and 5x + 4y = −3 →
  20. 20.7x + 3y = −78 and 3x + 7y = −62 →
  21. 21.x + 2y = 21 and 6x − 3y = 6 →
  22. 22.6x + 6y = 24 and 6x + 4y = 32 →
  23. 23.5x − 2y = 10 and x + 2y = 14 →
  24. 24.2x + 2y = 0 and 3x − 6y = 36 →
  25. 25.x − 2y = −11 and x + 3y = 14 →
  26. 26.4x + 8y = −28 and 8x + 4y = 28 →
  27. 27.4x − 2y = −24 and 5x − 3y = −31 →
  28. 28.5x + 2y = −44 and x + 5y = −18 →
  29. 29.2x + 5y = 24 and 6x − 6y = −54 →
  30. 30.6x + 3y = −45 and 2x + 4y = −6 →
  31. 31.x + 4y = 0 and 2x + 2y = −12 →
  32. 32.2x + 6y = 18 and 4x − y = 23 →
  33. 33.3x + 3y = −21 and x + 2y = −16 →
  34. 34.2x − 3y = −7 and 6x + y = −31 →
  35. 35.4x + 3y = 48 and 5x + 5y = 65 →
  36. 36.2x − 2y = −10 and 3x + 2y = 30 →
  37. 37.x + 3y = 4 and 4x + 3y = −2 →
  38. 38.3x + 9y = 42 and 9x + 3y = 78 →
  39. 39.5x + 5y = 40 and x + 5y = 28 →
  40. 40.4x − 2y = −20 and 3x + y = 0 →

Answer key

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

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