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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 40 · 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 − 2y = −8 and 4x − 6y = 0 →
  2. 2.5x + y = 2 and x + y = −6 →
  3. 3.x − 5y = −6 and 4x − 4y = 8 →
  4. 4.x − 5y = −48 and x + y = 6 →
  5. 5.2x + 4y = −6 and 4x + 2y = 18 →
  6. 6.x + 5y = −16 and 6x + 3y = −42 →
  7. 7.2x − 4y = −44 and 3x + 5y = 22 →
  8. 8.3x + 2y = 20 and 6x − 4y = −16 →
  9. 9.7x + 6y = −10 and 6x + 7y = −16 →
  10. 10.2x + 3y = −9 and 3x + 2y = −1 →
  11. 11.3x + 4y = 38 and 3x + 5y = 43 →
  12. 12.4x + y = 43 and x + 4y = 37 →
  13. 13.4x + 2y = 14 and 2x + 4y = 10 →
  14. 14.6x + 6y = 66 and x + 6y = 56 →
  15. 15.3x − 4y = 10 and 5x + 2y = −44 →
  16. 16.x + 5y = −18 and 6x − 2y = −44 →
  17. 17.4x + 6y = 22 and 6x − 3y = −3 →
  18. 18.3x − 6y = −27 and 2x + y = −8 →
  19. 19.2x + 2y = 32 and 2x + 5y = 53 →
  20. 20.4x + 3y = 39 and 3x + 4y = 31 →
  21. 21.6x + y = 28 and 6x − 6y = 0 →
  22. 22.8x + 7y = −48 and 7x + 8y = −57 →
  23. 23.x + 2y = 16 and 2x − 3y = −10 →
  24. 24.5x + 3y = −31 and 3x + 5y = −25 →
  25. 25.4x + y = 31 and 4x − 4y = 36 →
  26. 26.3x + 3y = 36 and 4x − 6y = −2 →
  27. 27.3x + 5y = 41 and 5x + 3y = 47 →
  28. 28.x − y = 2 and 6x − 5y = 17 →
  29. 29.3x + y = 21 and 2x + y = 16 →
  30. 30.5x + 9y = −20 and 9x + 5y = 20 →
  31. 31.5x + 7y = −8 and 7x + 5y = −16 →
  32. 32.2x + y = 11 and x + 2y = 16 →
  33. 33.4x + 7y = 35 and 7x + 4y = 53 →
  34. 34.4x + 4y = 16 and 3x + 6y = 18 →
  35. 35.2x + 3y = 14 and 5x + 4y = 7 →
  36. 36.3x + 2y = 20 and 5x + 5y = 45 →
  37. 37.3x + 4y = −5 and 5x − 2y = 35 →
  38. 38.5x − 5y = −55 and x + 3y = 21 →
  39. 39.5x + 7y = 66 and 7x + 5y = 54 →
  40. 40.5x + 6y = 34 and x − y = −2 →

Answer key

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

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