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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 273 · 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 − 5y = 21 and x + 5y = 21 →
  2. 2.6x − y = −27 and 4x + 4y = −4 →
  3. 3.x + 5y = 36 and x − 3y = −20 →
  4. 4.4x − 3y = 25 and 4x + 6y = 34 →
  5. 5.x − 2y = −3 and x − 3y = −8 →
  6. 6.4x + y = −21 and 2x + 4y = 14 →
  7. 7.3x − y = −30 and 2x + 2y = −12 →
  8. 8.x + 6y = 57 and 6x + 3y = 45 →
  9. 9.2x + y = 3 and 3x + 5y = 8 →
  10. 10.3x − y = 28 and 2x − 4y = 32 →
  11. 11.5x + 3y = −13 and 4x + 4y = −20 →
  12. 12.x − 2y = −11 and 6x + 5y = 53 →
  13. 13.9x + y = 27 and x + 9y = 83 →
  14. 14.x + 3y = 9 and 2x + y = 8 →
  15. 15.3x + y = −9 and 3x + 2y = −6 →
  16. 16.x + 5y = 49 and 5x + y = 53 →
  17. 17.4x − y = 18 and 2x + 6y = 48 →
  18. 18.6x − y = −20 and 6x − 5y = −28 →
  19. 19.x − 3y = −25 and 6x + 2y = −30 →
  20. 20.5x + 4y = 52 and 6x + 2y = 40 →
  21. 21.3x + 2y = −4 and 2x + 2y = −2 →
  22. 22.4x − 4y = −8 and 3x + 6y = 48 →
  23. 23.5x + 3y = −17 and 3x + 5y = −7 →
  24. 24.5x − 2y = −43 and 2x + 3y = −21 →
  25. 25.9x + y = 13 and x + 9y = 37 →
  26. 26.6x + 2y = −28 and 4x − 6y = −26 →
  27. 27.3x + 2y = −6 and 4x + 5y = −22 →
  28. 28.6x + 6y = 24 and 2x − 6y = −48 →
  29. 29.5x + 4y = 81 and 3x − 2y = 9 →
  30. 30.5x + 5y = 40 and 6x + 2y = 20 →
  31. 31.7x + 6y = −43 and 6x + 7y = −48 →
  32. 32.4x − y = 12 and 4x + 5y = −12 →
  33. 33.4x − 2y = −42 and 5x + 3y = −3 →
  34. 34.5x + 2y = 12 and x − 5y = 51 →
  35. 35.6x − 5y = 9 and 3x + 2y = 18 →
  36. 36.4x + 2y = 16 and 6x + 5y = 16 →
  37. 37.5x + 2y = 23 and 2x + 3y = 29 →
  38. 38.x + 3y = 20 and 2x + 4y = 26 →
  39. 39.8x + 5y = 77 and 5x + 8y = 53 →
  40. 40.4x − 4y = −8 and 2x + 4y = 32 →

Answer key

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

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