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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 907 · 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. 1.4x + 2y = −2 and 3x + 5y = 23 →
  2. 2.2x + 7y = 32 and 7x + 2y = 22 →
  3. 3.3x + 5y = 22 and x + 4y = 12 →
  4. 4.x + 4y = −22 and 4x + y = 2 →
  5. 5.x + 3y = −23 and 6x − 4y = 38 →
  6. 6.7x + y = 51 and x + 7y = 69 →
  7. 7.3x + 2y = 36 and 6x − 5y = 18 →
  8. 8.x + 6y = 43 and x + y = 3 →
  9. 9.6x + 6y = 18 and 2x + 5y = 12 →
  10. 10.2x − 3y = 20 and 3x + 2y = 4 →
  11. 11.9x + 4y = 33 and 4x + 9y = 58 →
  12. 12.8x + y = 40 and x + 8y = 68 →
  13. 13.5x − y = −21 and 2x − 5y = −36 →
  14. 14.6x + 3y = 0 and 5x + 3y = −1 →
  15. 15.5x − 3y = 41 and x + 4y = −24 →
  16. 16.x − 4y = −43 and x + 6y = 47 →
  17. 17.x + y = 11 and 4x − 2y = −4 →
  18. 18.3x + 2y = −1 and x + y = 2 →
  19. 19.2x − y = 22 and 5x − y = 46 →
  20. 20.3x + 5y = 21 and 6x − 5y = −3 →
  21. 21.3x + 5y = 64 and 4x − 5y = −8 →
  22. 22.6x + 9y = 51 and 9x + 6y = 39 →
  23. 23.2x − 6y = −16 and 6x − 2y = 32 →
  24. 24.3x + y = −4 and 2x − 5y = −14 →
  25. 25.4x + 6y = 34 and 6x + 3y = 21 →
  26. 26.4x + 5y = 72 and 4x + 3y = 56 →
  27. 27.5x + 4y = 39 and 4x + 5y = 33 →
  28. 28.x + y = 7 and 6x + 5y = 33 →
  29. 29.6x + 4y = 32 and 2x + 2y = 12 →
  30. 30.4x − 4y = −48 and 4x + 3y = 1 →
  31. 31.3x + 5y = 2 and 5x + 3y = 30 →
  32. 32.8x + 3y = 45 and 3x + 8y = 10 →
  33. 33.x − 5y = −10 and 3x + 3y = 24 →
  34. 34.8x + 4y = 48 and 4x + 8y = 0 →
  35. 35.4x + 3y = −33 and 4x + 6y = −54 →
  36. 36.2x + 9y = 62 and 9x + 2y = −29 →
  37. 37.x − 3y = −13 and x + y = 3 →
  38. 38.3x + 4y = 42 and 2x + 5y = 42 →
  39. 39.5x + 3y = 8 and 3x + 5y = 8 →
  40. 40.6x − y = 10 and 3x + y = 17 →

Answer key

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

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