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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 724 · 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. 1.3x − 3y = −12 and 6x + 5y = 53 →
  2. 2.5x + 3y = −36 and 4x − y = −22 →
  3. 3.6x − 5y = 4 and 3x + y = −5 →
  4. 4.8x + 9y = 59 and 9x + 8y = 60 →
  5. 5.6x + 3y = −51 and 3x + 6y = −57 →
  6. 6.6x + 2y = 30 and 5x + 2y = 22 →
  7. 7.4x + 6y = −52 and 6x + 4y = −58 →
  8. 8.5x + 3y = −6 and 3x + 5y = 6 →
  9. 9.2x + 5y = 20 and 4x − y = −26 →
  10. 10.5x + 4y = −14 and x + y = −2 →
  11. 11.6x + y = 54 and x + 6y = 44 →
  12. 12.4x + 3y = 11 and 4x − 3y = −19 →
  13. 13.4x + 2y = 34 and 4x − 2y = 22 →
  14. 14.5x + 9y = −79 and 9x + 5y = −75 →
  15. 15.5x + 6y = −23 and 3x − 5y = 55 →
  16. 16.4x + y = 13 and 5x − 3y = 12 →
  17. 17.9x + y = −45 and x + 9y = 75 →
  18. 18.3x − 3y = 33 and 3x + 5y = 9 →
  19. 19.6x + 6y = 6 and 4x + 3y = 1 →
  20. 20.7x + 6y = 60 and 6x + 7y = 57 →
  21. 21.2x + y = 9 and x + 2y = 0 →
  22. 22.2x + 4y = 10 and 4x + 2y = 32 →
  23. 23.2x − 3y = −3 and x + y = −9 →
  24. 24.2x + 5y = 34 and 3x − 6y = −30 →
  25. 25.x − y = 9 and 6x − 4y = 42 →
  26. 26.6x + 3y = 21 and 5x + 2y = 17 →
  27. 27.x + 3y = 17 and 6x + 4y = 46 →
  28. 28.x + y = −7 and 3x + 5y = −31 →
  29. 29.5x + 5y = −5 and 2x − 5y = −23 →
  30. 30.2x − y = 16 and 6x + 3y = 24 →
  31. 31.3x + y = −9 and x + 3y = 5 →
  32. 32.4x + 2y = 38 and 2x + 4y = 46 →
  33. 33.5x + 6y = 29 and 2x + 4y = 18 →
  34. 34.4x − 4y = 48 and 5x + 6y = −28 →
  35. 35.6x + 6y = 78 and 2x − 4y = −10 →
  36. 36.2x + 4y = 0 and 5x + 2y = −8 →
  37. 37.x + 4y = 17 and 4x + y = 23 →
  38. 38.6x + 4y = 56 and 4x + 6y = 64 →
  39. 39.7x + y = 49 and x + 7y = 55 →
  40. 40.3x + 2y = −2 and 4x + 5y = 16 →

Answer key

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

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