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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 418 · 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 + 3y = 49 and 4x − 5y = −20 →
  2. 2.7x + 9y = 72 and 9x + 7y = 88 →
  3. 3.8x + 9y = −35 and 9x + 8y = −33 →
  4. 4.2x + y = 9 and x + 4y = −20 →
  5. 5.3x + 4y = −21 and 6x + 6y = −30 →
  6. 6.6x − y = −60 and 2x + 6y = 18 →
  7. 7.3x + 8y = 35 and 8x + 3y = −35 →
  8. 8.5x − 6y = 56 and 2x + 2y = −4 →
  9. 9.5x + 5y = 60 and 5x − 3y = 4 →
  10. 10.6x + 9y = 60 and 9x + 6y = 60 →
  11. 11.3x + 5y = 42 and x − 5y = −6 →
  12. 12.6x − 2y = 24 and 3x + 6y = −9 →
  13. 13.6x − 2y = −42 and 6x + 3y = −57 →
  14. 14.x + 2y = 4 and 3x + y = 7 →
  15. 15.7x + 5y = 29 and 5x + 7y = 31 →
  16. 16.2x + y = 10 and 3x + 6y = 42 →
  17. 17.5x − 3y = −54 and 5x + 2y = −39 →
  18. 18.x + 5y = 41 and 5x + y = 13 →
  19. 19.6x + 6y = 72 and 4x + 5y = 53 →
  20. 20.6x + 4y = 36 and 4x + 6y = 34 →
  21. 21.8x + 5y = 66 and 5x + 8y = 51 →
  22. 22.5x + 6y = −9 and x − 4y = −7 →
  23. 23.7x + 3y = 1 and 3x + 7y = −51 →
  24. 24.5x + 2y = 56 and 3x + 2y = 40 →
  25. 25.5x + y = −7 and x + 5y = −11 →
  26. 26.x + 9y = 32 and 9x + y = 48 →
  27. 27.7x + 3y = 38 and 3x + 7y = 22 →
  28. 28.5x + 4y = −19 and 4x − 5y = −48 →
  29. 29.x − 4y = 39 and 6x − 3y = 45 →
  30. 30.x + 3y = 5 and 3x + y = −1 →
  31. 31.2x + 9y = 75 and 9x + 2y = −9 →
  32. 32.5x − y = 17 and x + 3y = 13 →
  33. 33.x + 3y = 0 and 6x − y = −19 →
  34. 34.5x + 4y = 42 and 4x + 5y = 48 →
  35. 35.7x + 5y = 24 and 5x + 7y = 48 →
  36. 36.3x + 2y = 16 and 2x + 3y = 4 →
  37. 37.x + 3y = 28 and 5x + y = 14 →
  38. 38.4x + 6y = 40 and 5x + y = 11 →
  39. 39.7x + 3y = 26 and 3x + 7y = −6 →
  40. 40.6x + 6y = 0 and x + 2y = −4 →

Answer key

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

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