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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 770 · 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 − y = −39 and 5x + 6y = 24 →
  2. 2.3x + 3y = −9 and x + 3y = −19 →
  3. 3.3x + 3y = 0 and x + 6y = 40 →
  4. 4.5x + 2y = 42 and 4x + 4y = 36 →
  5. 5.2x + 2y = 26 and 5x − y = 17 →
  6. 6.2x − 2y = 6 and 4x + 6y = 2 →
  7. 7.4x + y = 36 and x + 4y = 39 →
  8. 8.2x + 6y = −40 and 3x + 6y = −48 →
  9. 9.2x + 9y = 31 and 9x + 2y = 24 →
  10. 10.4x − 2y = −32 and 2x + 4y = 14 →
  11. 11.4x + 4y = 40 and 2x + 6y = 24 →
  12. 12.x + 5y = 21 and 5x + y = −15 →
  13. 13.3x + 3y = −21 and x − 6y = 56 →
  14. 14.x − y = 5 and 4x + 6y = −60 →
  15. 15.7x + 5y = 12 and 5x + 7y = 12 →
  16. 16.6x + 2y = 72 and 4x + 2y = 54 →
  17. 17.5x − 2y = −63 and 3x − 5y = −72 →
  18. 18.8x + y = 75 and x + 8y = 33 →
  19. 19.4x + 2y = 46 and 2x + 4y = 38 →
  20. 20.2x + y = 12 and x + 2y = 12 →
  21. 21.2x + 5y = 1 and 2x − 5y = −29 →
  22. 22.6x − 5y = 88 and 3x + 4y = −8 →
  23. 23.6x + 4y = 2 and 4x + 6y = 18 →
  24. 24.2x + 4y = 38 and 4x − 3y = −1 →
  25. 25.8x + 3y = 57 and 3x + 8y = 42 →
  26. 26.5x + 4y = 32 and 3x + y = 15 →
  27. 27.7x + 2y = 9 and 2x + 7y = 54 →
  28. 28.6x + 5y = 70 and 3x − 2y = −1 →
  29. 29.4x + 4y = 28 and x − 6y = 21 →
  30. 30.x + y = 8 and 4x − 3y = 18 →
  31. 31.5x + 6y = 58 and 3x + 4y = 38 →
  32. 32.4x − 5y = −33 and 5x + y = −34 →
  33. 33.5x − 4y = 6 and 3x − 4y = 2 →
  34. 34.4x − 6y = −80 and x − 4y = −40 →
  35. 35.2x + 5y = 22 and 3x + 2y = 22 →
  36. 36.x + 4y = 36 and 6x − 4y = 20 →
  37. 37.4x + 9y = −1 and 9x + 4y = 14 →
  38. 38.4x + y = −10 and x − 6y = −40 →
  39. 39.2x + 6y = 50 and 2x + 5y = 44 →
  40. 40.x + 2y = −5 and 5x + 3y = −39 →

Answer key

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

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