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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 424 · 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. 1.6x + 4y = 56 and 4x + 6y = 54 →
  2. 2.x − 5y = −32 and 2x − 6y = −40 →
  3. 3.4x + 2y = 34 and 5x − 4y = 23 →
  4. 4.x + 3y = 15 and 3x − 3y = −27 →
  5. 5.6x − 2y = 26 and 4x + 6y = −34 →
  6. 6.3x − 6y = 54 and 3x + 4y = −16 →
  7. 7.6x + 3y = −12 and 3x + 6y = 21 →
  8. 8.x + 4y = 2 and 3x − 3y = −9 →
  9. 9.x + 7y = −5 and 7x + y = 13 →
  10. 10.3x − 4y = 13 and 5x + y = 37 →
  11. 11.3x + 4y = 33 and 4x + 3y = 37 →
  12. 12.8x + y = 28 and x + 8y = −28 →
  13. 13.6x + 4y = −2 and 2x + 4y = −14 →
  14. 14.6x + 5y = 26 and 5x + 6y = 29 →
  15. 15.3x + y = −33 and x + 3y = −27 →
  16. 16.5x + y = 31 and 2x + 2y = 6 →
  17. 17.2x + 6y = 24 and 3x − 3y = 24 →
  18. 18.9x + 7y = −22 and 7x + 9y = −42 →
  19. 19.6x + 7y = 76 and 7x + 6y = 80 →
  20. 20.2x − y = −2 and 4x + 5y = 24 →
  21. 21.4x + 5y = −13 and 4x + y = 7 →
  22. 22.5x − 6y = −60 and 5x + 6y = 0 →
  23. 23.4x + y = −8 and x + 5y = −21 →
  24. 24.2x + y = 22 and 3x + 3y = 45 →
  25. 25.6x − 4y = −22 and x + 5y = 19 →
  26. 26.2x + 2y = 20 and 4x − 2y = 4 →
  27. 27.3x + 4y = 19 and 4x + 3y = 16 →
  28. 28.2x − 3y = −20 and x − 2y = −14 →
  29. 29.2x − 5y = −28 and 3x + 3y = −21 →
  30. 30.6x − 5y = 40 and 2x + 2y = 6 →
  31. 31.5x + 4y = 29 and 4x + 5y = 25 →
  32. 32.3x − 4y = 2 and 6x − 2y = 28 →
  33. 33.x + 2y = 8 and 2x + y = 10 →
  34. 34.3x + 4y = 5 and 4x + 3y = 2 →
  35. 35.5x + 6y = 19 and 2x + y = 2 →
  36. 36.4x + 4y = 0 and 4x − y = 20 →
  37. 37.4x − 6y = 46 and x + y = −1 →
  38. 38.5x + 6y = 33 and x + 6y = 21 →
  39. 39.3x − 2y = 20 and 4x + y = 34 →
  40. 40.5x + 2y = 31 and 3x + 4y = 27 →

Answer key

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

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