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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 330 · 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. 1.3x + y = 7 and x + 3y = 5 →
  2. 2.3x + 5y = 29 and 5x + 3y = 43 →
  3. 3.6x + 8y = −18 and 8x + 6y = −10 →
  4. 4.x − 5y = −2 and 4x + 5y = −33 →
  5. 5.5x − 6y = −52 and x − y = −10 →
  6. 6.x + 4y = −34 and 4x + 6y = −56 →
  7. 7.2x + y = 18 and 2x + 3y = 30 →
  8. 8.4x + 8y = 44 and 8x + 4y = −20 →
  9. 9.4x + 8y = −84 and 8x + 4y = −84 →
  10. 10.2x + 9y = −51 and 9x + 2y = 40 →
  11. 11.6x + 5y = 13 and 5x + 6y = 9 →
  12. 12.x + 5y = −26 and 2x + 4y = −22 →
  13. 13.8x + y = −14 and x + 8y = 14 →
  14. 14.x − 2y = 0 and x − 6y = −4 →
  15. 15.6x + 6y = 48 and 4x − 6y = 22 →
  16. 16.3x + 5y = 1 and 4x + 2y = 6 →
  17. 17.3x − y = 18 and 4x + 2y = 54 →
  18. 18.2x + 2y = −4 and x + 6y = 23 →
  19. 19.8x + 2y = 46 and 2x + 8y = 34 →
  20. 20.2x + y = 12 and x + 2y = 12 →
  21. 21.3x − 2y = −7 and x + 2y = 11 →
  22. 22.3x + 7y = 1 and 7x + 3y = −51 →
  23. 23.x + 6y = 27 and 2x + y = −1 →
  24. 24.3x + y = 9 and 3x − 2y = 0 →
  25. 25.5x − 5y = −50 and 3x − 2y = −21 →
  26. 26.6x − 6y = 12 and 6x − 3y = 18 →
  27. 27.3x + 6y = 9 and 4x + 5y = 18 →
  28. 28.2x + 2y = 0 and 4x − 2y = 36 →
  29. 29.6x + 2y = 10 and 2x + 6y = −18 →
  30. 30.5x − 2y = −33 and 4x − 3y = −25 →
  31. 31.6x + y = 18 and 6x − 5y = −18 →
  32. 32.3x + y = −34 and x + 3y = −30 →
  33. 33.2x + 2y = 12 and 2x + y = 4 →
  34. 34.3x + 3y = 6 and 2x − 2y = 0 →
  35. 35.2x + 6y = 38 and x − 3y = −35 →
  36. 36.5x − 6y = 63 and 3x + 3y = −15 →
  37. 37.4x + 3y = −4 and 5x + 6y = −23 →
  38. 38.4x − 4y = 12 and 4x + 3y = 26 →
  39. 39.3x + 7y = 66 and 7x + 3y = 74 →
  40. 40.x + 4y = 29 and 2x − y = 4 →

Answer key

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

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