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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 431 · 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. 1.8x + 3y = 74 and 3x + 8y = 69 →
  2. 2.4x − 2y = 14 and 3x − 3y = 3 →
  3. 3.2x + 7y = 65 and 7x + 2y = 25 →
  4. 4.2x + 6y = 50 and 2x + 2y = 26 →
  5. 5.6x + 7y = 98 and 7x + 6y = 97 →
  6. 6.6x + 7y = −89 and 7x + 6y = −93 →
  7. 7.4x + 8y = −60 and 8x + 4y = −84 →
  8. 8.2x + 2y = 2 and x + 6y = 16 →
  9. 9.7x + 2y = −45 and 2x + 7y = 45 →
  10. 10.9x + 5y = 72 and 5x + 9y = 96 →
  11. 11.2x − 5y = 26 and 2x + 5y = 6 →
  12. 12.3x + 2y = 15 and 5x + 4y = 27 →
  13. 13.8x + y = 26 and x + 8y = −44 →
  14. 14.2x + y = 27 and 4x − 6y = −18 →
  15. 15.3x − 3y = 42 and x + 6y = −35 →
  16. 16.3x + 2y = −26 and 4x + 5y = −51 →
  17. 17.4x − y = −27 and 2x − 3y = −21 →
  18. 18.4x − 4y = 4 and x + y = −11 →
  19. 19.2x − 2y = 12 and x − 4y = 27 →
  20. 20.5x + y = 19 and x + 5y = −25 →
  21. 21.6x + 7y = 55 and 7x + 6y = 49 →
  22. 22.4x + 3y = −14 and x − 2y = −20 →
  23. 23.x + 8y = 49 and 8x + y = 14 →
  24. 24.5x + 3y = 49 and x + 6y = 26 →
  25. 25.4x + 3y = 23 and 3x + 2y = 18 →
  26. 26.3x + 4y = 7 and 2x + 3y = 6 →
  27. 27.2x + 6y = 30 and 5x + y = 33 →
  28. 28.x + 6y = −11 and 6x + y = 39 →
  29. 29.5x − 2y = −3 and 3x + 2y = 11 →
  30. 30.6x + 8y = 46 and 8x + 6y = 66 →
  31. 31.x + 5y = 47 and 5x + 3y = 37 →
  32. 32.x + 3y = 10 and 3x + y = −10 →
  33. 33.5x + y = −41 and x + 2y = −10 →
  34. 34.3x + y = 27 and x + y = 11 →
  35. 35.4x − 4y = −48 and 5x − y = −40 →
  36. 36.x + 5y = 12 and 4x + y = 29 →
  37. 37.7x + 4y = 64 and 4x + 7y = 79 →
  38. 38.2x − 5y = 9 and x + 6y = −4 →
  39. 39.3x + 5y = 60 and 5x + 3y = 52 →
  40. 40.4x − y = 9 and 4x + 6y = 58 →

Answer key

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

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