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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 249 · 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 + y = −28 and 6x + 6y = −84 →
  2. 2.x + 6y = 32 and x + 2y = 12 →
  3. 3.2x − 4y = −34 and 3x − 5y = −42 →
  4. 4.9x + y = 51 and x + 9y = 59 →
  5. 5.4x − 4y = 44 and 3x + 6y = 6 →
  6. 6.x − 3y = −18 and x + 4y = 3 →
  7. 7.6x + 2y = −20 and 2x + y = −4 →
  8. 8.6x + 2y = 36 and 4x + 2y = 30 →
  9. 9.6x + y = −22 and x + 6y = 43 →
  10. 10.x + 3y = 19 and 5x + y = 11 →
  11. 11.2x + 2y = −20 and x + 3y = −24 →
  12. 12.8x + 2y = 0 and 2x + 8y = −30 →
  13. 13.2x + 4y = 40 and 4x + 5y = 53 →
  14. 14.2x + 4y = 28 and 5x + 2y = 22 →
  15. 15.4x + 2y = −22 and 4x + y = −23 →
  16. 16.2x + 2y = 10 and 4x − y = 10 →
  17. 17.x + 3y = 5 and 3x + y = −9 →
  18. 18.2x + 2y = −4 and 3x + 6y = 15 →
  19. 19.4x − 5y = −7 and 5x − 4y = −11 →
  20. 20.4x + 6y = 18 and 2x − 4y = −54 →
  21. 21.2x + 4y = 22 and x − y = −16 →
  22. 22.2x + 7y = −5 and 7x + 2y = −40 →
  23. 23.2x + 5y = 23 and x − 5y = −11 →
  24. 24.4x + 5y = 3 and 5x + 4y = 15 →
  25. 25.6x + 4y = −22 and 2x + 3y = −4 →
  26. 26.x + 9y = 69 and 9x + y = −19 →
  27. 27.3x + y = 13 and 4x + 3y = 24 →
  28. 28.x − 4y = −26 and x + 3y = 30 →
  29. 29.x + 4y = −19 and 4x + y = −1 →
  30. 30.6x + 2y = 62 and 2x + 6y = 58 →
  31. 31.4x + 2y = 26 and x − 2y = −6 →
  32. 32.5x + y = −5 and 6x − 4y = −32 →
  33. 33.x + y = 0 and 2x + 4y = −2 →
  34. 34.3x − 5y = 44 and 6x + 2y = 4 →
  35. 35.6x + y = 30 and 3x + 2y = 6 →
  36. 36.5x + 4y = 23 and 6x − y = 16 →
  37. 37.8x + y = −24 and x + 8y = −66 →
  38. 38.2x + 5y = −24 and 5x − 6y = 51 →
  39. 39.7x + 2y = 21 and 2x + 7y = −39 →
  40. 40.x − 3y = −3 and 2x − 3y = 3 →

Answer key

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

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