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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 87 · 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 + 6y = −52 and x + 3y = −23 →
  2. 2.5x − 5y = −55 and 4x + 5y = −8 →
  3. 3.6x + y = 44 and x − 2y = 3 →
  4. 4.5x + 7y = 58 and 7x + 5y = 62 →
  5. 5.9x + 3y = 39 and 3x + 9y = −51 →
  6. 6.4x + 6y = 38 and 6x + 4y = 12 →
  7. 7.x + 5y = −22 and 3x + 2y = −14 →
  8. 8.3x + 4y = 16 and 4x + 3y = 19 →
  9. 9.7x + 3y = 2 and 3x + 7y = 18 →
  10. 10.5x + 6y = 51 and x + 4y = 27 →
  11. 11.5x − y = 38 and 2x − 6y = 60 →
  12. 12.8x + 2y = 10 and 2x + 8y = −20 →
  13. 13.5x + 4y = −36 and 4x + 5y = −36 →
  14. 14.2x − y = 14 and 3x + 6y = 6 →
  15. 15.5x + 3y = 64 and 4x + 4y = 64 →
  16. 16.9x + 3y = 27 and 3x + 9y = 33 →
  17. 17.x + 9y = −80 and 9x + y = −80 →
  18. 18.4x + y = 34 and 4x − y = 22 →
  19. 19.3x + 3y = −3 and 3x − y = −23 →
  20. 20.3x − 4y = 0 and 2x + 5y = 46 →
  21. 21.5x + 2y = 17 and 2x + y = 7 →
  22. 22.5x + 8y = 93 and 8x + 5y = 102 →
  23. 23.9x + 2y = 16 and 2x + 9y = −5 →
  24. 24.x + 6y = −16 and 6x + y = 44 →
  25. 25.7x + 4y = −18 and 4x + 7y = 18 →
  26. 26.9x + y = 4 and x + 9y = −44 →
  27. 27.6x − 6y = 42 and 2x + y = −13 →
  28. 28.3x + 5y = 58 and 4x + y = 32 →
  29. 29.3x + 2y = 1 and 2x + 3y = 4 →
  30. 30.5x + 9y = −76 and 9x + 5y = −36 →
  31. 31.x + 4y = 13 and 4x + y = 7 →
  32. 32.x + 2y = −7 and 3x + 4y = −13 →
  33. 33.3x + 2y = 14 and 3x + y = 10 →
  34. 34.2x + 4y = 2 and x + 4y = 9 →
  35. 35.x + y = −2 and 3x − 6y = −42 →
  36. 36.4x − 2y = 42 and 5x + 3y = 14 →
  37. 37.2x − 3y = 21 and x + 6y = −12 →
  38. 38.4x + y = 24 and 4x + 3y = 8 →
  39. 39.2x + y = 9 and 3x + y = 13 →
  40. 40.2x + 6y = 30 and x − 4y = −13 →

Answer key

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

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