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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 743 · 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 + 2y = 32 and 4x + 6y = 52 →
  2. 2.3x + 7y = −23 and 7x + 3y = 13 →
  3. 3.3x + 3y = 0 and 5x + 4y = 9 →
  4. 4.6x + y = 22 and 3x + 4y = 4 →
  5. 5.4x + 2y = 8 and x − 4y = 20 →
  6. 6.2x − 3y = 1 and 6x − 2y = 10 →
  7. 7.6x + 5y = 15 and 4x − 3y = 29 →
  8. 8.6x − 2y = 12 and 6x + 2y = 36 →
  9. 9.x + 3y = −15 and 3x − 2y = −1 →
  10. 10.9x + 6y = 102 and 6x + 9y = 93 →
  11. 11.4x + 2y = 20 and 4x + 6y = 52 →
  12. 12.5x − y = 22 and 5x − 6y = 7 →
  13. 13.x − 3y = −31 and 2x − y = −22 →
  14. 14.6x − 4y = 80 and 4x + 6y = −16 →
  15. 15.x + 5y = −20 and 4x + y = 15 →
  16. 16.4x + 3y = −42 and 3x + 4y = −35 →
  17. 17.5x − 3y = −2 and 3x + y = 24 →
  18. 18.2x + y = 11 and x + 2y = 13 →
  19. 19.6x + 7y = −52 and 7x + 6y = −52 →
  20. 20.5x + 2y = 24 and 2x + 5y = 18 →
  21. 21.5x + 3y = 34 and 2x + 5y = 44 →
  22. 22.2x + 4y = −18 and 5x + 4y = −15 →
  23. 23.3x + 7y = −35 and 7x + 3y = 25 →
  24. 24.7x + 9y = −112 and 9x + 7y = −112 →
  25. 25.2x + 5y = 25 and 5x + 2y = 31 →
  26. 26.x + 4y = 38 and 6x + y = 21 →
  27. 27.4x − 5y = −17 and 2x + 6y = 34 →
  28. 28.4x + 2y = −2 and 5x − 4y = −9 →
  29. 29.7x + 9y = 101 and 9x + 7y = 107 →
  30. 30.5x + 9y = −32 and 9x + 5y = 32 →
  31. 31.3x + 5y = 43 and 3x + y = 23 →
  32. 32.5x − 6y = −7 and 3x + 3y = 9 →
  33. 33.4x + 4y = 40 and x + 4y = 34 →
  34. 34.3x + 2y = −7 and 2x + 3y = −18 →
  35. 35.4x + y = 14 and 5x − 4y = −14 →
  36. 36.5x + 3y = −42 and 5x + y = −44 →
  37. 37.2x − y = −13 and x + y = −5 →
  38. 38.5x + 5y = −5 and 5x + 6y = −3 →
  39. 39.4x − 4y = 68 and 3x − 2y = 43 →
  40. 40.3x + 3y = −6 and 5x + 2y = −1 →

Answer key

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

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