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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 254 · 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 + 5y = 65 and 5x + 3y = 49 →
  2. 2.3x − 5y = 19 and 3x + 6y = −3 →
  3. 3.3x + 8y = 88 and 8x + 3y = 88 →
  4. 4.x − 5y = −26 and 2x + y = 25 →
  5. 5.2x + 3y = 23 and x + 2y = 15 →
  6. 6.x + 6y = 56 and 2x − 2y = 0 →
  7. 7.3x + 5y = −16 and 2x + 2y = 0 →
  8. 8.x + 2y = −7 and 2x + y = 1 →
  9. 9.9x + y = 9 and x + 9y = −79 →
  10. 10.5x + 3y = 34 and 4x + 4y = 32 →
  11. 11.5x − 4y = 32 and 6x + 2y = 52 →
  12. 12.4x + 3y = 5 and 3x + 2y = 6 →
  13. 13.5x − 3y = −19 and 5x + 6y = −82 →
  14. 14.x + 2y = −1 and 2x + 2y = −10 →
  15. 15.x + 3y = 13 and 3x + y = 15 →
  16. 16.2x − 2y = −14 and 3x − 2y = −23 →
  17. 17.3x + 4y = −2 and x + 2y = −2 →
  18. 18.3x − y = 10 and 3x − 4y = 22 →
  19. 19.5x + 3y = 14 and 5x + y = −2 →
  20. 20.2x + 5y = 43 and 5x + 5y = 70 →
  21. 21.7x + 9y = −15 and 9x + 7y = −33 →
  22. 22.6x + y = −16 and 6x + 5y = −8 →
  23. 23.4x + y = −15 and x + 4y = 30 →
  24. 24.5x + y = 32 and x − 4y = −2 →
  25. 25.5x − y = 20 and 5x − 2y = 15 →
  26. 26.2x + y = 23 and x + 2y = 19 →
  27. 27.3x − 6y = −30 and 6x + y = −47 →
  28. 28.6x − 6y = −12 and 2x + 2y = 8 →
  29. 29.2x + 3y = 43 and 3x + 2y = 42 →
  30. 30.3x + 6y = −24 and 6x + 3y = 6 →
  31. 31.8x + 6y = 74 and 6x + 8y = 80 →
  32. 32.6x + 4y = −70 and 4x + 6y = −60 →
  33. 33.3x + 4y = −17 and 2x + 4y = −18 →
  34. 34.8x + 7y = 119 and 7x + 8y = 121 →
  35. 35.x + 3y = −23 and 3x + y = −21 →
  36. 36.4x + y = 15 and 5x + 2y = 24 →
  37. 37.4x − 2y = −26 and 4x + y = 1 →
  38. 38.6x + y = −51 and x + 6y = 9 →
  39. 39.4x + 2y = 14 and 4x − 5y = −7 →
  40. 40.5x + 3y = 25 and 5x + 4y = 20 →

Answer key

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

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