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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 803 · 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. 1.6x − 5y = 23 and 4x + 4y = −36 →
  2. 2.4x + 4y = 24 and x + 2y = 9 →
  3. 3.2x + 3y = 29 and 3x + 2y = 31 →
  4. 4.2x − y = 10 and x − y = 2 →
  5. 5.x + 5y = 47 and 3x − 3y = −3 →
  6. 6.3x − 4y = −44 and 5x − y = −28 →
  7. 7.7x + 2y = −58 and 2x + 7y = −23 →
  8. 8.6x + y = −4 and x + 6y = 11 →
  9. 9.6x + 4y = −22 and 6x + 3y = −21 →
  10. 10.x + 7y = −3 and 7x + y = 27 →
  11. 11.4x + y = 11 and 2x + 3y = 13 →
  12. 12.3x − 3y = 3 and 2x − 6y = 30 →
  13. 13.3x + y = 1 and 3x + 2y = −4 →
  14. 14.8x + 4y = 84 and 4x + 8y = 60 →
  15. 15.5x + 8y = 112 and 8x + 5y = 109 →
  16. 16.5x − y = 15 and 3x + 5y = −19 →
  17. 17.x − y = −7 and 6x + 6y = 18 →
  18. 18.2x + y = −20 and 4x + 5y = −58 →
  19. 19.8x + 3y = −16 and 3x + 8y = 49 →
  20. 20.x − 5y = 46 and 5x − 2y = 23 →
  21. 21.5x − 2y = 38 and 2x + y = 17 →
  22. 22.8x + y = −49 and x + 8y = 49 →
  23. 23.3x − 3y = 0 and 2x + 5y = 49 →
  24. 24.5x + 2y = 51 and x + 2y = 15 →
  25. 25.3x + 6y = 9 and 6x + 3y = −18 →
  26. 26.4x + 2y = 22 and 3x − 2y = −8 →
  27. 27.3x + 3y = 24 and 4x + 2y = 28 →
  28. 28.4x + 3y = −28 and 2x + 5y = −42 →
  29. 29.5x − y = 8 and 6x − 5y = 2 →
  30. 30.x + 3y = 11 and 3x + y = −7 →
  31. 31.7x + 2y = −3 and 2x + 7y = 57 →
  32. 32.3x − 5y = 36 and x + 4y = −5 →
  33. 33.4x − 3y = 11 and 3x + 4y = 2 →
  34. 34.4x + 9y = 45 and 9x + 4y = −45 →
  35. 35.6x − 4y = 64 and 4x + 6y = −18 →
  36. 36.x + 3y = 22 and 4x + 3y = 34 →
  37. 37.3x + 5y = −31 and 6x − 2y = −38 →
  38. 38.5x + 4y = 24 and 6x + y = 25 →
  39. 39.3x − 3y = −21 and 6x + 4y = 48 →
  40. 40.6x + 3y = 18 and 3x + 6y = 0 →

Answer key

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

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