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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 738 · 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.x + 3y = 8 and 6x + 2y = 32 →
  2. 2.5x + 2y = 15 and x + 6y = 31 →
  3. 3.3x − y = 1 and 5x + 3y = −17 →
  4. 4.7x + 6y = 69 and 6x + 7y = 61 →
  5. 5.2x + 4y = −14 and 5x + y = 1 →
  6. 6.x + 8y = 18 and 8x + y = 18 →
  7. 7.9x + 4y = 74 and 4x + 9y = 69 →
  8. 8.3x + 5y = 40 and 2x − 4y = −10 →
  9. 9.4x + 4y = 16 and 2x − 2y = 24 →
  10. 10.2x + 5y = 45 and 4x − 2y = 6 →
  11. 11.2x − 2y = −6 and 5x + 3y = −7 →
  12. 12.6x + 9y = 21 and 9x + 6y = 24 →
  13. 13.3x + 2y = −16 and 5x + y = −36 →
  14. 14.2x − 2y = 6 and 3x + 3y = 45 →
  15. 15.6x + y = 27 and x + 3y = 30 →
  16. 16.7x + 6y = −20 and 6x + 7y = −19 →
  17. 17.4x + 5y = 4 and 6x − 3y = 48 →
  18. 18.5x − 5y = 50 and x + y = −6 →
  19. 19.4x − 6y = 6 and 4x + 6y = 66 →
  20. 20.8x + 5y = −7 and 5x + 8y = −19 →
  21. 21.2x + 7y = −10 and 7x + 2y = 55 →
  22. 22.2x − 2y = −14 and 2x + 5y = 21 →
  23. 23.9x + 4y = 2 and 4x + 9y = −28 →
  24. 24.3x + 2y = 12 and 2x + 3y = 23 →
  25. 25.5x + 5y = 20 and 5x + 4y = 22 →
  26. 26.3x + 6y = 48 and 2x + y = 20 →
  27. 27.x + 4y = −19 and 4x + y = −16 →
  28. 28.7x + 4y = 36 and 4x + 7y = 30 →
  29. 29.3x + 6y = 12 and 5x − 2y = 44 →
  30. 30.5x + 5y = 75 and 3x + 5y = 59 →
  31. 31.5x + 4y = −9 and 4x + 5y = 0 →
  32. 32.5x − 3y = −5 and 4x + 5y = 33 →
  33. 33.5x + 3y = 27 and 3x + 5y = 13 →
  34. 34.2x + y = 6 and x + 2y = 6 →
  35. 35.2x − 4y = −10 and 2x + 6y = 50 →
  36. 36.x + 5y = 13 and 3x + 6y = 30 →
  37. 37.x − 3y = 10 and 2x − 4y = 16 →
  38. 38.2x − 4y = −2 and x − y = −3 →
  39. 39.x + 4y = −1 and x + 2y = 1 →
  40. 40.4x − y = −28 and 4x − 2y = −24 →

Answer key

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

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