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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 144 · 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. 1.4x + 3y = 25 and 5x − 5y = 5 →
  2. 2.5x + 4y = 16 and 6x + 5y = 21 →
  3. 3.7x + 2y = −52 and 2x + 7y = −2 →
  4. 4.x − 2y = −14 and x + 2y = 18 →
  5. 5.5x + 3y = 49 and 2x + y = 19 →
  6. 6.7x + 6y = 12 and 6x + 7y = 1 →
  7. 7.9x + 2y = 25 and 2x + 9y = 74 →
  8. 8.4x + 5y = −3 and x + 6y = 23 →
  9. 9.4x + 2y = 18 and 6x + 2y = 28 →
  10. 10.x + 7y = 59 and 7x + y = 29 →
  11. 11.5x + 2y = −39 and 2x + 5y = −24 →
  12. 12.x + y = −1 and 5x − 2y = −12 →
  13. 13.x − 2y = 9 and 4x + 5y = −3 →
  14. 14.2x + 3y = −7 and x − y = −6 →
  15. 15.5x + 5y = −20 and 2x + y = 1 →
  16. 16.2x + 5y = 12 and 5x + 2y = 9 →
  17. 17.x + 9y = 31 and 9x + y = −41 →
  18. 18.6x + 2y = 60 and 6x + y = 51 →
  19. 19.8x + 3y = −45 and 3x + 8y = −10 →
  20. 20.5x − 6y = 8 and 2x + 3y = −40 →
  21. 21.6x + y = −19 and 6x + 2y = −26 →
  22. 22.9x + 5y = 63 and 5x + 9y = 91 →
  23. 23.5x − 5y = 40 and 2x + 3y = 21 →
  24. 24.5x + y = 31 and x − 2y = −7 →
  25. 25.4x + y = 9 and x + 4y = 21 →
  26. 26.3x + 2y = 22 and 5x + 3y = 34 →
  27. 27.x − 6y = 37 and 3x + y = −3 →
  28. 28.4x + 6y = 84 and 3x + 4y = 59 →
  29. 29.4x + 2y = 24 and x − 5y = 28 →
  30. 30.8x + 3y = −61 and 3x + 8y = −16 →
  31. 31.3x − 4y = −17 and 4x − 2y = −16 →
  32. 32.6x + 6y = −6 and 3x − 4y = −59 →
  33. 33.4x − 2y = 16 and 2x + 2y = 32 →
  34. 34.5x − 5y = −70 and 5x − y = −34 →
  35. 35.4x − y = 41 and 4x + 3y = 21 →
  36. 36.5x − 6y = −23 and 2x + 5y = 50 →
  37. 37.3x + y = 4 and x + 3y = −4 →
  38. 38.3x + 2y = 7 and 2x + 2y = 6 →
  39. 39.5x + 5y = 35 and 3x + y = 19 →
  40. 40.6x − 3y = 9 and x − 4y = −9 →

Answer key

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

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