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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 885 · 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 − y = −13 and x + 5y = 10 →
  2. 2.5x + 6y = 52 and 6x + 5y = 58 →
  3. 3.2x − 3y = 25 and 6x + 6y = −60 →
  4. 4.x + 5y = 0 and 5x + y = 24 →
  5. 5.x − 3y = −22 and 5x − 4y = −22 →
  6. 6.6x + 2y = 12 and 5x + 6y = 23 →
  7. 7.5x + 5y = −20 and 4x − y = 29 →
  8. 8.2x − 5y = −4 and x − 3y = −3 →
  9. 9.3x − 5y = 10 and 2x + 5y = 15 →
  10. 10.3x + y = 4 and x + 3y = 4 →
  11. 11.7x + 9y = −17 and 9x + 7y = −31 →
  12. 12.x + 3y = 20 and 3x + y = 28 →
  13. 13.5x + 3y = −60 and x + 3y = −24 →
  14. 14.9x + y = 19 and x + 9y = 11 →
  15. 15.9x + 3y = −30 and 3x + 9y = 54 →
  16. 16.5x + 2y = −8 and 4x + 2y = −4 →
  17. 17.3x + 5y = 44 and 4x + 4y = 40 →
  18. 18.2x + 5y = −4 and 3x + 2y = 16 →
  19. 19.x + 3y = −19 and x + 4y = −27 →
  20. 20.5x + 4y = 69 and 3x + 3y = 45 →
  21. 21.4x + 5y = 23 and 4x − 6y = −10 →
  22. 22.6x + 3y = 30 and 5x + 3y = 23 →
  23. 23.3x + 6y = 3 and 6x + 3y = −3 →
  24. 24.5x − y = 16 and 6x − y = 20 →
  25. 25.6x + y = 58 and 2x + 5y = 38 →
  26. 26.x + 6y = 56 and 6x + y = 21 →
  27. 27.6x − 6y = −36 and x + 5y = 42 →
  28. 28.5x − 4y = 26 and 6x + 6y = −12 →
  29. 29.9x + 6y = −30 and 6x + 9y = 0 →
  30. 30.2x + y = 14 and 2x + 3y = 22 →
  31. 31.5x − 5y = −5 and x + y = 3 →
  32. 32.2x − 6y = −18 and 2x − y = −13 →
  33. 33.4x − y = −14 and 2x + y = −4 →
  34. 34.4x + 5y = 48 and 3x − y = −2 →
  35. 35.3x + 5y = 26 and 5x + 6y = 27 →
  36. 36.6x + 5y = 58 and 2x − 5y = 6 →
  37. 37.5x + 4y = 37 and 4x + 5y = 35 →
  38. 38.4x + y = −15 and x + 4y = 15 →
  39. 39.x + 7y = 15 and 7x + y = 57 →
  40. 40.2x − 5y = −33 and x + 2y = 24 →

Answer key

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

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