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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 225 · 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 + 7y = 3 and 7x + 3y = −33 →
  2. 2.6x − 3y = 54 and 4x + 4y = −12 →
  3. 3.5x + 5y = 30 and 2x − 4y = 18 →
  4. 4.2x − y = 14 and 2x + 5y = −22 →
  5. 5.x + 4y = −2 and x + 6y = 0 →
  6. 6.9x + 8y = 34 and 8x + 9y = 34 →
  7. 7.5x + 3y = 43 and 4x − 2y = 30 →
  8. 8.6x + 6y = 60 and 2x + y = 14 →
  9. 9.9x + 8y = 44 and 8x + 9y = 41 →
  10. 10.x + 4y = 12 and 3x − 2y = −20 →
  11. 11.2x − 3y = 32 and 5x + 2y = 23 →
  12. 12.2x + 6y = 34 and x + 5y = 25 →
  13. 13.3x + 2y = −22 and 2x + 3y = −18 →
  14. 14.6x + y = 54 and x + 6y = 44 →
  15. 15.x + 2y = −3 and 4x − y = −3 →
  16. 16.2x + y = 9 and x + 5y = −27 →
  17. 17.x + 6y = −3 and 6x + y = −53 →
  18. 18.5x + 3y = −11 and 4x − 2y = 22 →
  19. 19.3x − 6y = 48 and 3x + 5y = −18 →
  20. 20.5x + 2y = 42 and 4x − 2y = 30 →
  21. 21.5x + 4y = 18 and 4x + 3y = 14 →
  22. 22.4x + 5y = 57 and 6x + 4y = 68 →
  23. 23.7x + 4y = −77 and 4x + 7y = −77 →
  24. 24.3x + 4y = 45 and x + 6y = 43 →
  25. 25.x + 2y = 8 and 5x + 3y = 33 →
  26. 26.2x + 3y = 10 and 3x + 2y = 10 →
  27. 27.4x − 4y = 32 and 5x + 2y = 33 →
  28. 28.4x + y = −7 and 5x − 6y = −45 →
  29. 29.x + 2y = −6 and 2x + y = 0 →
  30. 30.4x + 2y = −8 and 5x − 4y = −36 →
  31. 31.6x − 6y = −66 and 2x − y = −13 →
  32. 32.2x + 3y = 41 and x + y = 16 →
  33. 33.3x − y = 5 and x + 3y = −5 →
  34. 34.6x − 2y = −36 and 4x − y = −27 →
  35. 35.9x + 4y = 52 and 4x + 9y = 52 →
  36. 36.x + y = 6 and 6x − 6y = −24 →
  37. 37.3x − 5y = 2 and 6x + 4y = 74 →
  38. 38.3x + y = −1 and x + y = 1 →
  39. 39.5x + y = 18 and 4x + 3y = −1 →
  40. 40.2x + 7y = −49 and 7x + 2y = 31 →

Answer key

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

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