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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 139 · 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. 1.2x + y = 14 and x + 2y = 4 →
  2. 2.3x + y = 16 and x + 6y = 28 →
  3. 3.x − 3y = −3 and x − 5y = −11 →
  4. 4.x − y = 7 and x + 4y = 12 →
  5. 5.8x + 2y = 60 and 2x + 8y = −30 →
  6. 6.4x − 4y = −8 and 5x + 5y = −70 →
  7. 7.x + 2y = 18 and 5x + 3y = 41 →
  8. 8.2x + 4y = −12 and 2x + y = 0 →
  9. 9.2x + 3y = 21 and 6x + 5y = 59 →
  10. 10.3x + 9y = −48 and 9x + 3y = 48 →
  11. 11.2x + 6y = −36 and 6x + 2y = 4 →
  12. 12.4x + 4y = −24 and 6x + 2y = −16 →
  13. 13.9x + 6y = −129 and 6x + 9y = −126 →
  14. 14.7x + 8y = 46 and 8x + 7y = 44 →
  15. 15.4x + 3y = −10 and 2x + 6y = 22 →
  16. 16.x − 2y = −7 and 6x + y = 23 →
  17. 17.3x + 3y = 30 and 6x − 2y = 20 →
  18. 18.2x + 4y = 36 and x − y = 0 →
  19. 19.x + 3y = 5 and 4x + 2y = 10 →
  20. 20.x + 3y = 8 and 3x − 2y = 2 →
  21. 21.x + 9y = 67 and 9x + y = 43 →
  22. 22.7x + 9y = 44 and 9x + 7y = 52 →
  23. 23.7x + y = 23 and x + 7y = 17 →
  24. 24.6x + 5y = 1 and 5x + 6y = −1 →
  25. 25.6x + 8y = 56 and 8x + 6y = 70 →
  26. 26.x − y = 1 and 4x − 3y = 10 →
  27. 27.x + y = 11 and 3x + 6y = 45 →
  28. 28.4x + 3y = −42 and 3x − 3y = 0 →
  29. 29.4x − 4y = −24 and 5x − y = −42 →
  30. 30.6x + 3y = 48 and 4x + 4y = 28 →
  31. 31.6x + 7y = −21 and 7x + 6y = −31 →
  32. 32.5x + 2y = 9 and 2x + 5y = 12 →
  33. 33.5x − 5y = −50 and 3x + 4y = −9 →
  34. 34.2x − 4y = −30 and 3x − 4y = −35 →
  35. 35.2x − y = −19 and 2x + y = −17 →
  36. 36.3x + 6y = 60 and x + y = 11 →
  37. 37.3x + 2y = 26 and 5x + 2y = 42 →
  38. 38.9x + 8y = −137 and 8x + 9y = −135 →
  39. 39.6x − 5y = −42 and x − 5y = −32 →
  40. 40.5x + 5y = 25 and 4x + y = 17 →

Answer key

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

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