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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 411 · 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.x − 6y = 18 and 4x − y = 26 →
  2. 2.2x + 3y = −9 and 4x + 5y = −21 →
  3. 3.6x + 8y = 42 and 8x + 6y = 42 →
  4. 4.5x − 4y = 32 and 3x − 2y = 20 →
  5. 5.3x + 7y = −11 and 7x + 3y = 41 →
  6. 6.2x + 5y = 55 and 3x − 6y = −39 →
  7. 7.4x + 5y = 28 and 3x − 2y = −25 →
  8. 8.4x + y = 30 and 2x + y = 12 →
  9. 9.2x + 3y = 43 and 5x + 4y = 76 →
  10. 10.3x + 4y = −46 and 4x + 3y = −45 →
  11. 11.2x − 3y = −34 and 4x + 2y = −4 →
  12. 12.x + 2y = 7 and 4x − 4y = 16 →
  13. 13.x − 4y = −11 and 2x + 5y = −9 →
  14. 14.x − 2y = −1 and 3x − 3y = 3 →
  15. 15.5x − 4y = −31 and 3x + 2y = −23 →
  16. 16.x + 5y = 14 and 2x − 5y = −32 →
  17. 17.2x + y = 10 and 5x + 3y = 28 →
  18. 18.5x + 2y = 33 and 2x + 5y = 30 →
  19. 19.x − 6y = −56 and 4x − 2y = −48 →
  20. 20.x + 2y = 5 and 6x + 4y = 14 →
  21. 21.3x − y = 29 and 2x + 2y = 6 →
  22. 22.x + 4y = −17 and x − 2y = 13 →
  23. 23.8x + y = 35 and x + 8y = −35 →
  24. 24.6x + 3y = 15 and 6x + 4y = 16 →
  25. 25.8x + 6y = −18 and 6x + 8y = −10 →
  26. 26.2x + 3y = 31 and 3x + 2y = 29 →
  27. 27.x − 4y = −34 and 6x + y = 21 →
  28. 28.5x − 6y = 51 and 4x + 3y = 33 →
  29. 29.8x + 5y = −19 and 5x + 8y = 32 →
  30. 30.3x + 4y = 8 and x + 2y = 8 →
  31. 31.x + 2y = 12 and 4x + 3y = 33 →
  32. 32.3x + y = −3 and 3x + 6y = 27 →
  33. 33.x + 5y = −42 and 5x + y = 6 →
  34. 34.5x + 6y = −1 and 6x + 5y = −10 →
  35. 35.3x + 6y = 57 and 3x + y = 12 →
  36. 36.5x + y = 22 and x − 5y = 20 →
  37. 37.6x + 2y = 38 and 6x + 4y = 46 →
  38. 38.8x + 2y = 30 and 2x + 8y = 60 →
  39. 39.5x − 2y = 39 and 6x + 4y = 34 →
  40. 40.5x + 3y = 34 and 3x + 5y = 46 →

Answer key

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

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