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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 660 · 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 + 5y = 51 and x − 4y = −20 →
  2. 2.4x + 2y = −42 and 3x − 3y = 9 →
  3. 3.3x + 5y = 31 and 3x + y = 23 →
  4. 4.2x + 9y = −32 and 9x + 2y = 10 →
  5. 5.5x + 2y = 14 and x − y = 14 →
  6. 6.6x + 4y = 64 and 5x + 3y = 52 →
  7. 7.x + 8y = 11 and 8x + y = 25 →
  8. 8.5x + 4y = 47 and 4x + 5y = 52 →
  9. 9.4x + 6y = −2 and 4x + 4y = 4 →
  10. 10.5x − 6y = 45 and 5x − 5y = 40 →
  11. 11.x + 9y = 32 and 9x + y = 48 →
  12. 12.5x + 4y = −11 and 3x + 4y = 3 →
  13. 13.5x + 7y = −4 and 7x + 5y = 4 →
  14. 14.x + 2y = 18 and 2x + y = 12 →
  15. 15.4x + 3y = 43 and 5x − 6y = −34 →
  16. 16.6x + 3y = 57 and 3x + 6y = 42 →
  17. 17.3x + 2y = 11 and 2x + 3y = 9 →
  18. 18.5x + y = 26 and 6x + 4y = 34 →
  19. 19.3x + 3y = 0 and x + 3y = −10 →
  20. 20.2x + 3y = −11 and 4x − y = 41 →
  21. 21.4x + 5y = 22 and 3x − 3y = 30 →
  22. 22.3x + 5y = −22 and 5x + 2y = −43 →
  23. 23.2x + 7y = 47 and 7x + 2y = 7 →
  24. 24.2x + 6y = 26 and 5x + 3y = 41 →
  25. 25.6x + 3y = 21 and x + 3y = 11 →
  26. 26.3x − 4y = 0 and 2x + y = −22 →
  27. 27.7x + 2y = −51 and 2x + 7y = 24 →
  28. 28.2x + 3y = 20 and 2x + 6y = 26 →
  29. 29.4x + y = 7 and x − 2y = 22 →
  30. 30.3x + 5y = 30 and 4x − 5y = 5 →
  31. 31.4x + 2y = −8 and 2x + 4y = −28 →
  32. 32.2x + y = 14 and x + 2y = 10 →
  33. 33.x + 6y = 18 and 6x + y = 38 →
  34. 34.3x + 2y = 35 and 5x + y = 42 →
  35. 35.x + 4y = 14 and 4x + y = −4 →
  36. 36.x + 2y = 12 and 2x + y = 3 →
  37. 37.x − 6y = −47 and 5x − 2y = −11 →
  38. 38.6x + 5y = 53 and x + 4y = 31 →
  39. 39.2x + 9y = 19 and 9x + 2y = 47 →
  40. 40.8x + 7y = 22 and 7x + 8y = 23 →

Answer key

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

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