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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 226 · 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. 1.4x − 6y = 18 and 5x + 6y = 63 →
  2. 2.4x − 6y = −2 and 6x − 4y = −28 →
  3. 3.7x + 5y = −28 and 5x + 7y = −44 →
  4. 4.2x − y = 1 and 4x − 5y = −13 →
  5. 5.5x − 6y = −20 and 4x + 3y = 23 →
  6. 6.2x − 2y = −4 and 6x + 4y = 28 →
  7. 7.2x − 4y = −8 and 3x + y = 23 →
  8. 8.5x + 4y = 24 and 3x − 3y = 36 →
  9. 9.x + 6y = −27 and 4x − 5y = 37 →
  10. 10.7x + 4y = −33 and 4x + 7y = 0 →
  11. 11.7x + 8y = 79 and 8x + 7y = 71 →
  12. 12.6x + y = 47 and x + 6y = 37 →
  13. 13.6x + 5y = 35 and 5x + 6y = 31 →
  14. 14.8x + 9y = 38 and 9x + 8y = 30 →
  15. 15.2x + 4y = −4 and 4x + 2y = 22 →
  16. 16.x + 3y = 25 and 4x + 5y = 44 →
  17. 17.x − 6y = 5 and 5x + 4y = −9 →
  18. 18.2x + y = 4 and x − 2y = −13 →
  19. 19.2x + 3y = −8 and 3x + 2y = 3 →
  20. 20.2x + 7y = 24 and 7x + 2y = −6 →
  21. 21.4x − 2y = 26 and 5x − 3y = 34 →
  22. 22.7x + 8y = 78 and 8x + 7y = 72 →
  23. 23.2x + 4y = 16 and 6x + 4y = 32 →
  24. 24.3x + 6y = −3 and 6x + 3y = −42 →
  25. 25.5x + 8y = 46 and 8x + 5y = 58 →
  26. 26.3x + 5y = 19 and 6x + 6y = 30 →
  27. 27.2x + 5y = −6 and 5x − 2y = −44 →
  28. 28.5x + 5y = −30 and 2x + 5y = −9 →
  29. 29.6x + 3y = 66 and 3x − 5y = −6 →
  30. 30.3x + 2y = 30 and 4x − 4y = 0 →
  31. 31.2x − 3y = −20 and 2x + y = −4 →
  32. 32.8x + 9y = 73 and 9x + 8y = 80 →
  33. 33.2x − 3y = −3 and 3x + 6y = 69 →
  34. 34.2x + 6y = 2 and x − 5y = 9 →
  35. 35.5x + 5y = 60 and 4x − 4y = 16 →
  36. 36.4x + 6y = 72 and 2x + 5y = 48 →
  37. 37.9x + 3y = 60 and 3x + 9y = 12 →
  38. 38.6x + 4y = 64 and 4x + 6y = 56 →
  39. 39.4x − 5y = −36 and 6x + 5y = −4 →
  40. 40.6x − 4y = 6 and 6x + 2y = 60 →

Answer key

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

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