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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 508 · 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. 1.6x + y = −50 and 2x − 6y = 34 →
  2. 2.6x + 6y = 54 and 3x + y = 15 →
  3. 3.4x + 2y = −20 and 5x − y = −4 →
  4. 4.x − y = −11 and 4x − 6y = −48 →
  5. 5.4x + 5y = −67 and x − 5y = 27 →
  6. 6.4x + 6y = 18 and x + y = 4 →
  7. 7.2x + 5y = 7 and 5x − 4y = 1 →
  8. 8.6x + 5y = −32 and 5x + 6y = −34 →
  9. 9.8x + 9y = 73 and 9x + 8y = 80 →
  10. 10.4x + 3y = 8 and 3x + 4y = 13 →
  11. 11.3x − 6y = 18 and 2x + 4y = −4 →
  12. 12.7x + 4y = 51 and 4x + 7y = 48 →
  13. 13.2x − 2y = −4 and 3x + 6y = 21 →
  14. 14.4x + y = 29 and 6x + y = 45 →
  15. 15.8x + 9y = −37 and 9x + 8y = −31 →
  16. 16.x + 2y = 11 and 2x + 5y = 25 →
  17. 17.3x − 5y = 62 and 5x − 4y = 73 →
  18. 18.4x + 3y = 21 and 3x + 4y = 21 →
  19. 19.7x + 2y = 11 and 2x + 7y = 61 →
  20. 20.4x + 4y = 32 and 2x + y = 11 →
  21. 21.2x + 7y = 44 and 7x + 2y = 64 →
  22. 22.2x − 5y = −11 and 5x − 2y = −17 →
  23. 23.5x + 6y = −27 and 6x + 5y = −39 →
  24. 24.x + y = −5 and 5x − 5y = 65 →
  25. 25.3x − 6y = −60 and x + y = 1 →
  26. 26.x + y = 7 and 2x − y = −1 →
  27. 27.3x + 7y = 90 and 7x + 3y = 90 →
  28. 28.4x + y = 27 and x + 4y = 18 →
  29. 29.4x + 3y = 48 and 3x + 5y = 47 →
  30. 30.2x + 3y = 12 and 3x + y = 11 →
  31. 31.3x + 6y = 3 and 2x − 3y = −33 →
  32. 32.2x + y = 11 and 2x − 5y = −7 →
  33. 33.3x − 3y = −30 and 4x + 2y = 8 →
  34. 34.7x + 4y = −88 and 4x + 7y = −88 →
  35. 35.4x + 3y = 40 and 3x + 3y = 36 →
  36. 36.5x + 7y = 71 and 7x + 5y = 61 →
  37. 37.5x + 6y = 59 and x − 4y = −35 →
  38. 38.x + 2y = 21 and x + 6y = 57 →
  39. 39.x + y = 5 and 4x − 4y = 4 →
  40. 40.6x − 5y = −73 and 5x + 2y = −30 →

Answer key

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

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