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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 450 · 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 = 58 and 3x + y = 17 →
  2. 2.7x + 3y = 10 and 3x + 7y = −30 →
  3. 3.x + y = −8 and x + 4y = −5 →
  4. 4.5x + 2y = 2 and x + y = 4 →
  5. 5.6x + 3y = −39 and 4x + 6y = −38 →
  6. 6.5x + 8y = 59 and 8x + 5y = 71 →
  7. 7.x + 5y = 38 and 5x + y = 22 →
  8. 8.x + 2y = 2 and 2x + y = −8 →
  9. 9.3x + 4y = 4 and 2x + y = −4 →
  10. 10.2x − 6y = 44 and 6x + 5y = −29 →
  11. 11.6x + 2y = 34 and 6x + 6y = 42 →
  12. 12.2x + y = 7 and x + 2y = 11 →
  13. 13.x − 3y = −27 and x − 2y = −20 →
  14. 14.4x − 2y = −34 and 3x + 5y = 7 →
  15. 15.4x − y = 17 and 3x + 3y = 9 →
  16. 16.x − 4y = −24 and 5x − 3y = 16 →
  17. 17.2x + 3y = 27 and 3x + 2y = 33 →
  18. 18.3x − 5y = 2 and 6x − y = 22 →
  19. 19.8x + 4y = 60 and 4x + 8y = 72 →
  20. 20.4x + 4y = 36 and 6x + 2y = 30 →
  21. 21.8x + 2y = 38 and 2x + 8y = −28 →
  22. 22.3x + 6y = −15 and 6x + 3y = 33 →
  23. 23.4x + 3y = −4 and 3x + 4y = 11 →
  24. 24.5x + 6y = 23 and x − 6y = −53 →
  25. 25.2x + 6y = 18 and 2x + 4y = 16 →
  26. 26.3x + 4y = −22 and 4x + 3y = −13 →
  27. 27.5x − 6y = −59 and x − y = −11 →
  28. 28.4x + 6y = 24 and 6x + 4y = 26 →
  29. 29.2x − y = 9 and 2x + 6y = 44 →
  30. 30.6x + 5y = 39 and 6x + 4y = 42 →
  31. 31.8x + 7y = −31 and 7x + 8y = −44 →
  32. 32.2x + 4y = 14 and 4x + 2y = 16 →
  33. 33.6x + 4y = −6 and 2x + 5y = 20 →
  34. 34.x + 3y = −24 and 3x + y = −32 →
  35. 35.3x + 3y = 6 and x + 5y = −6 →
  36. 36.x + 4y = 7 and 6x + 4y = 22 →
  37. 37.2x − 5y = −42 and 2x + 4y = 30 →
  38. 38.5x + 5y = 15 and 6x + 3y = 0 →
  39. 39.3x + 4y = −24 and 3x − 4y = 0 →
  40. 40.5x + 6y = 3 and 6x + 5y = 19 →

Answer key

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

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