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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 555 · 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. 1.5x + 9y = 0 and 9x + 5y = 56 →
  2. 2.5x + y = 33 and 3x + 6y = 63 →
  3. 3.4x + y = 13 and x + 6y = −14 →
  4. 4.5x + 6y = −19 and 6x + 5y = −14 →
  5. 5.x − y = 1 and x − 2y = 3 →
  6. 6.3x + 6y = 3 and 6x + 3y = 42 →
  7. 7.4x + 3y = 16 and 3x + 4y = 19 →
  8. 8.4x + y = 15 and x + 4y = −30 →
  9. 9.3x − 4y = 3 and 4x + 6y = 72 →
  10. 10.x − 5y = −34 and 6x − 3y = −69 →
  11. 11.3x + 2y = 37 and 4x − y = 20 →
  12. 12.x − 2y = 26 and 3x + 2y = 6 →
  13. 13.2x + 3y = 14 and 4x + 3y = 10 →
  14. 14.5x + y = 6 and x + 5y = −42 →
  15. 15.2x + 7y = 25 and 7x + 2y = 20 →
  16. 16.2x + 3y = 30 and 3x − 2y = 19 →
  17. 17.2x + 4y = 14 and 5x + 2y = 27 →
  18. 18.4x + 6y = −18 and x + 6y = −27 →
  19. 19.2x − 3y = −6 and x − 5y = −17 →
  20. 20.3x + 9y = 87 and 9x + 3y = 69 →
  21. 21.3x + 6y = 66 and 6x + 3y = 69 →
  22. 22.4x + y = 13 and 5x + y = 16 →
  23. 23.2x + 2y = 14 and x + 2y = 12 →
  24. 24.2x + 4y = −14 and 5x − 4y = 21 →
  25. 25.3x + 6y = −33 and x + 4y = −29 →
  26. 26.3x + 4y = −40 and x + 2y = −16 →
  27. 27.8x + 2y = 44 and 2x + 8y = 26 →
  28. 28.3x − 2y = −8 and 5x − 2y = −4 →
  29. 29.5x − 6y = −24 and 2x − 2y = −10 →
  30. 30.2x + 4y = 18 and 4x + 2y = 30 →
  31. 31.x + 6y = 43 and x − 3y = −29 →
  32. 32.3x + 6y = 69 and 6x + 3y = 57 →
  33. 33.x + 5y = −36 and 5x + y = 36 →
  34. 34.3x − y = 8 and x + y = 0 →
  35. 35.5x − 4y = 4 and 3x + 4y = −36 →
  36. 36.4x + 6y = −8 and 4x − 6y = 40 →
  37. 37.x + 6y = −56 and 6x + y = −21 →
  38. 38.7x + 6y = 6 and 6x + 7y = 20 →
  39. 39.6x + 5y = 37 and 5x + 6y = 29 →
  40. 40.x + 6y = −29 and 6x + y = 1 →

Answer key

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

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