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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 766 · 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. 1.3x − 3y = −42 and x + 2y = 7 →
  2. 2.9x + 8y = −36 and 8x + 9y = −49 →
  3. 3.2x − 5y = 41 and 3x + 5y = −1 →
  4. 4.6x + 9y = 93 and 9x + 6y = 72 →
  5. 5.2x + 2y = 22 and 4x + 6y = 48 →
  6. 6.3x + 5y = −11 and 5x + 3y = 3 →
  7. 7.x + 7y = 52 and 7x + y = 28 →
  8. 8.5x + 6y = −52 and 6x − 2y = −44 →
  9. 9.3x + 5y = −14 and 4x − 2y = 42 →
  10. 10.3x − 2y = −25 and 4x − 6y = −50 →
  11. 11.4x + 2y = 26 and 2x + 4y = 28 →
  12. 12.x + 6y = 20 and 6x + y = 50 →
  13. 13.6x + y = 39 and 3x + 6y = 3 →
  14. 14.6x + 3y = 30 and 6x + 2y = 36 →
  15. 15.2x + 3y = −14 and 6x + 2y = 14 →
  16. 16.3x + 5y = 4 and 6x + 2y = −8 →
  17. 17.4x − y = 7 and 5x − 6y = 4 →
  18. 18.3x − 6y = 81 and 6x + 5y = 9 →
  19. 19.2x + 6y = 36 and x − y = −14 →
  20. 20.5x + 4y = 23 and x + 6y = 41 →
  21. 21.x + 6y = 25 and 3x + 3y = 15 →
  22. 22.2x − 2y = −24 and 6x − 2y = −36 →
  23. 23.6x + y = 11 and 3x − 4y = −17 →
  24. 24.2x + 5y = 9 and x + 4y = 9 →
  25. 25.8x + 5y = −66 and 5x + 8y = −51 →
  26. 26.x + 2y = −17 and x − 2y = 15 →
  27. 27.4x + 4y = −40 and 4x + 3y = −37 →
  28. 28.x − 6y = −42 and 3x + 5y = 12 →
  29. 29.x + 4y = 7 and 4x + y = −2 →
  30. 30.8x + 9y = 49 and 9x + 8y = 53 →
  31. 31.3x − 2y = 0 and 5x − 4y = −2 →
  32. 32.8x + 7y = 135 and 7x + 8y = 135 →
  33. 33.5x + 6y = 46 and 6x + 5y = 53 →
  34. 34.x − 5y = 14 and x + 5y = −16 →
  35. 35.x + 3y = 0 and 2x − y = 14 →
  36. 36.5x + 8y = −3 and 8x + 5y = −36 →
  37. 37.4x − y = 28 and 6x − 6y = 6 →
  38. 38.6x + 6y = 36 and 5x − 6y = −69 →
  39. 39.2x − 4y = −28 and x + y = 10 →
  40. 40.3x − 2y = 6 and 5x + 4y = 32 →

Answer key

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

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