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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 359 · 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 + 6y = −12 and 4x + 2y = −18 →
  2. 2.9x + 8y = −99 and 8x + 9y = −105 →
  3. 3.x + 2y = −15 and 5x − 6y = 37 →
  4. 4.6x + 3y = −6 and 3x + 6y = −21 →
  5. 5.3x − 5y = 31 and 5x + y = 33 →
  6. 6.7x + 4y = 10 and 4x + 7y = 34 →
  7. 7.3x + 4y = −25 and 4x + y = −29 →
  8. 8.5x + 4y = 9 and 4x + 5y = −9 →
  9. 9.2x + 5y = −43 and 5x + 2y = −13 →
  10. 10.3x + 4y = −3 and 5x − 6y = 71 →
  11. 11.6x − 3y = −9 and 5x − 6y = −4 →
  12. 12.x − 2y = −5 and 2x − 2y = −6 →
  13. 13.3x + 5y = 58 and 4x + 2y = 40 →
  14. 14.2x + 8y = 30 and 8x + 2y = 60 →
  15. 15.6x + 4y = 62 and 4x + 6y = 58 →
  16. 16.6x + 5y = 8 and 2x − 5y = −24 →
  17. 17.6x + 7y = 85 and 7x + 6y = 84 →
  18. 18.6x + 7y = 97 and 7x + 6y = 98 →
  19. 19.2x + 2y = 16 and 3x + 5y = 26 →
  20. 20.3x − 4y = 25 and 5x + 2y = 7 →
  21. 21.4x + 2y = 34 and 2x + 4y = 32 →
  22. 22.5x + 3y = −8 and 3x + 5y = 24 →
  23. 23.5x + 9y = 75 and 9x + 5y = 79 →
  24. 24.7x + 5y = 47 and 5x + 7y = 37 →
  25. 25.x + 9y = −20 and 9x + y = −20 →
  26. 26.6x + 6y = 84 and 5x + 4y = 63 →
  27. 27.2x − 4y = −20 and 2x + y = 10 →
  28. 28.6x + 2y = −14 and 2x + 3y = 14 →
  29. 29.6x − 2y = 6 and 4x + 6y = 26 →
  30. 30.6x + y = 3 and 5x − 3y = 14 →
  31. 31.3x + 8y = −77 and 8x + 3y = −77 →
  32. 32.8x + y = 14 and x + 8y = 49 →
  33. 33.3x + 6y = −51 and 6x + 3y = −21 →
  34. 34.3x − 2y = −30 and 2x − 3y = −35 →
  35. 35.8x + 7y = −6 and 7x + 8y = −9 →
  36. 36.3x + 3y = −9 and 2x + 5y = −27 →
  37. 37.3x + 7y = 67 and 7x + 3y = 63 →
  38. 38.4x + 5y = 56 and x − 4y = −7 →
  39. 39.x + 7y = −40 and 7x + y = 8 →
  40. 40.2x + 3y = 17 and 4x + 5y = 29 →

Answer key

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

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