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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 910 · 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 + 6y = −12 and 4x − 6y = −68 →
  2. 2.6x + 9y = 75 and 9x + 6y = 45 →
  3. 3.4x − 4y = 8 and 2x + 4y = 46 →
  4. 4.3x + 3y = −15 and 4x + 6y = −16 →
  5. 5.8x + 5y = −17 and 5x + 8y = −35 →
  6. 6.2x + 2y = 0 and 4x + 2y = 12 →
  7. 7.5x + 4y = −31 and x + y = −8 →
  8. 8.9x + 3y = 24 and 3x + 9y = 48 →
  9. 9.2x + y = −8 and x + 2y = −1 →
  10. 10.8x + 2y = −2 and 2x + 8y = −68 →
  11. 11.5x + 2y = 26 and 2x + 5y = −19 →
  12. 12.3x + 3y = 33 and x + 2y = 19 →
  13. 13.4x − y = 10 and x − 2y = 6 →
  14. 14.x + 9y = 35 and 9x + y = −5 →
  15. 15.3x + 6y = 60 and 6x + 3y = 48 →
  16. 16.x + y = −3 and 5x + 6y = −12 →
  17. 17.8x + y = 47 and x + 8y = 61 →
  18. 18.6x + y = 13 and 4x − 5y = −31 →
  19. 19.5x + 3y = 52 and x + y = 12 →
  20. 20.5x + y = −2 and x + 5y = −34 →
  21. 21.5x − y = −48 and 4x + 4y = −24 →
  22. 22.6x + 5y = 15 and 3x − y = 18 →
  23. 23.5x + 3y = 35 and x + y = 9 →
  24. 24.6x + 2y = −62 and 5x − 5y = −5 →
  25. 25.2x − 4y = −36 and 2x + 2y = −6 →
  26. 26.2x + 5y = 37 and x − 2y = −13 →
  27. 27.2x + 4y = 10 and 2x − 4y = 2 →
  28. 28.x + 3y = −26 and 3x + y = −14 →
  29. 29.4x + 2y = −4 and 5x + 2y = −2 →
  30. 30.6x + 4y = 66 and 2x + 4y = 46 →
  31. 31.x + 5y = 38 and 4x + 4y = 40 →
  32. 32.2x + 3y = 20 and 2x + 2y = 16 →
  33. 33.x + 2y = −8 and 6x + 4y = −40 →
  34. 34.9x + 3y = −60 and 3x + 9y = −36 →
  35. 35.2x − y = 14 and 3x + 3y = −6 →
  36. 36.5x − y = 18 and 4x + 5y = −3 →
  37. 37.6x + y = −15 and 4x + y = −9 →
  38. 38.4x − 6y = −64 and 4x − 2y = −40 →
  39. 39.3x + y = −21 and x + 2y = −2 →
  40. 40.2x − y = 9 and x − 3y = 12 →

Answer key

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

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