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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 109 · 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 = 3 and 5x + 6y = −3 →
  2. 2.5x + 6y = −37 and 4x + 5y = −31 →
  3. 3.3x + 2y = 20 and 2x + 3y = 15 →
  4. 4.2x + 4y = −8 and 4x − 2y = −6 →
  5. 5.x + 2y = 18 and 6x + y = 31 →
  6. 6.6x + 4y = 16 and 5x + 6y = 16 →
  7. 7.5x + 2y = 11 and 6x − y = 37 →
  8. 8.6x + 9y = 21 and 9x + 6y = 24 →
  9. 9.5x + 4y = 61 and 6x + 4y = 66 →
  10. 10.2x + 5y = −35 and x − 6y = 59 →
  11. 11.5x − 3y = 16 and 5x − 2y = 9 →
  12. 12.6x + y = −3 and 5x − 2y = 23 →
  13. 13.6x − y = −2 and 2x + 6y = −26 →
  14. 14.7x + 4y = 73 and 4x + 7y = 70 →
  15. 15.3x + 2y = −17 and 2x + 3y = −18 →
  16. 16.6x + 8y = 50 and 8x + 6y = 62 →
  17. 17.4x + 5y = −15 and 2x + 6y = −32 →
  18. 18.6x − 2y = −18 and x − 2y = −13 →
  19. 19.6x − 3y = −66 and 5x + 3y = −22 →
  20. 20.9x + 4y = 66 and 4x + 9y = 51 →
  21. 21.5x + 8y = −55 and 8x + 5y = −49 →
  22. 22.6x + 3y = −9 and 3x + 6y = −36 →
  23. 23.6x + y = 7 and 2x + 5y = 7 →
  24. 24.6x + 2y = −66 and x − 5y = 37 →
  25. 25.x + 7y = −12 and 7x + y = 12 →
  26. 26.x + 2y = 17 and 2x + y = 22 →
  27. 27.3x + y = −21 and x − 3y = 13 →
  28. 28.4x + 4y = −20 and x + 2y = −14 →
  29. 29.x − 2y = −12 and 3x − 3y = −9 →
  30. 30.6x + 9y = 48 and 9x + 6y = 27 →
  31. 31.4x + 7y = 6 and 7x + 4y = 27 →
  32. 32.2x + 6y = −34 and 5x + 3y = −13 →
  33. 33.6x + 6y = −24 and 2x − 6y = −48 →
  34. 34.3x − y = −5 and 3x + 4y = 35 →
  35. 35.6x + 5y = 17 and 6x − 6y = 6 →
  36. 36.3x − 4y = 11 and 4x + y = −36 →
  37. 37.x + 4y = 22 and 2x + 2y = 2 →
  38. 38.x + 4y = 5 and 6x − 3y = −51 →
  39. 39.x − 6y = −28 and 3x + 6y = 36 →
  40. 40.x + 2y = 14 and 2x + y = 19 →

Answer key

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

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