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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 987 · 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 = 19 and 3x + 3y = 33 →
  2. 2.2x + 5y = 57 and 5x + 2y = 48 →
  3. 3.x − 3y = −25 and 3x + 4y = 42 →
  4. 4.4x + 6y = −30 and 5x − y = 39 →
  5. 5.5x − 6y = 24 and 2x − 3y = 9 →
  6. 6.2x + 4y = 10 and x + 4y = 1 →
  7. 7.6x + 2y = 36 and x − 6y = −13 →
  8. 8.4x − 2y = 14 and 6x + 5y = −19 →
  9. 9.2x + y = −17 and x + 2y = −16 →
  10. 10.5x + 7y = −44 and 7x + 5y = −52 →
  11. 11.x − 3y = −28 and 4x + 4y = 32 →
  12. 12.6x − 4y = 18 and 2x − 3y = 11 →
  13. 13.3x + y = 24 and 6x + y = 42 →
  14. 14.x − 4y = 22 and 4x + 3y = 12 →
  15. 15.6x + 2y = 4 and 2x + y = 4 →
  16. 16.6x + 5y = 14 and 3x − 5y = 22 →
  17. 17.4x + 5y = −14 and 2x + 3y = −10 →
  18. 18.3x + y = −4 and 2x − 3y = −32 →
  19. 19.x − y = −6 and 2x + 4y = 42 →
  20. 20.8x + 2y = 24 and 2x + 8y = 66 →
  21. 21.x + 8y = −3 and 8x + y = 39 →
  22. 22.2x + 4y = −18 and 5x − 3y = 33 →
  23. 23.x + y = 1 and x − y = −17 →
  24. 24.2x + 9y = 74 and 9x + 2y = 25 →
  25. 25.3x + 5y = 10 and 2x − 6y = 16 →
  26. 26.2x + y = 16 and 4x + y = 26 →
  27. 27.2x + 6y = 54 and 6x + 2y = 50 →
  28. 28.3x − 2y = −10 and 4x + 6y = −22 →
  29. 29.5x − 2y = 61 and 3x − 2y = 43 →
  30. 30.3x − 2y = 21 and 2x + 5y = 33 →
  31. 31.9x + y = −44 and x + 9y = −76 →
  32. 32.8x + 6y = 26 and 6x + 8y = 30 →
  33. 33.8x + 5y = 55 and 5x + 8y = 49 →
  34. 34.x + 6y = 10 and 3x + 6y = 18 →
  35. 35.5x + 6y = −8 and 4x + 2y = 2 →
  36. 36.5x + 3y = 20 and 5x − 2y = 45 →
  37. 37.5x + 4y = 63 and 6x − 3y = 21 →
  38. 38.4x + 3y = 2 and 4x − 5y = 50 →
  39. 39.2x + 7y = −39 and 7x + 2y = 21 →
  40. 40.2x + 2y = −16 and 6x + 3y = −39 →

Answer key

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

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