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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 710 · 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. 1.2x + 5y = 14 and 2x + 2y = 8 →
  2. 2.2x − 2y = 20 and x + y = 8 →
  3. 3.x + 4y = 44 and 2x + 5y = 61 →
  4. 4.3x + 8y = 47 and 8x + 3y = −3 →
  5. 5.5x + 2y = 44 and 3x + 6y = 60 →
  6. 6.5x − 4y = −33 and x + 6y = −27 →
  7. 7.2x − 5y = 23 and 2x + 3y = 15 →
  8. 8.8x + 7y = 37 and 7x + 8y = 38 →
  9. 9.2x − 6y = −22 and 3x + 4y = −20 →
  10. 10.4x + 5y = 59 and 6x + y = 43 →
  11. 11.2x + y = 11 and x + 2y = 19 →
  12. 12.2x + y = 18 and 6x − 6y = 0 →
  13. 13.4x − 5y = 49 and 4x − 6y = 54 →
  14. 14.x + 4y = 23 and 4x + y = 2 →
  15. 15.2x + 4y = 2 and 6x + y = 39 →
  16. 16.x + 7y = 12 and 7x + y = 36 →
  17. 17.2x + 9y = 31 and 9x + 2y = 24 →
  18. 18.x − 5y = −44 and 5x + 2y = 23 →
  19. 19.x − 3y = −3 and 5x − 2y = 24 →
  20. 20.9x + 6y = 93 and 6x + 9y = 87 →
  21. 21.x + 3y = 26 and 4x − y = 0 →
  22. 22.6x − y = 21 and 2x − 5y = 21 →
  23. 23.3x + 5y = 32 and 5x + 3y = 16 →
  24. 24.x + 8y = 33 and 8x + y = 12 →
  25. 25.4x − 6y = 16 and x + 6y = 19 →
  26. 26.5x − 2y = 12 and x + 4y = 42 →
  27. 27.2x − y = −13 and 6x + y = −19 →
  28. 28.6x + 5y = −36 and 5x + 6y = −41 →
  29. 29.3x − y = 12 and 4x + 6y = −28 →
  30. 30.5x − 4y = −3 and 4x + 4y = 12 →
  31. 31.4x + 6y = 52 and 6x + 3y = 54 →
  32. 32.8x + 4y = 32 and 4x + 8y = −20 →
  33. 33.5x − 5y = 40 and 3x − 4y = 23 →
  34. 34.2x + 3y = 39 and 3x + 4y = 55 →
  35. 35.2x + y = 15 and 3x − 6y = 0 →
  36. 36.4x + y = 15 and 2x − 5y = −9 →
  37. 37.3x + 6y = −3 and x − 4y = −7 →
  38. 38.6x − 3y = 9 and 5x − 4y = −3 →
  39. 39.6x + 3y = 36 and 3x − 2y = −3 →
  40. 40.2x + 9y = −51 and 9x + 2y = −37 →

Answer key

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

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