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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 920 · 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. 1.2x + 6y = −16 and 2x − 2y = 24 →
  2. 2.2x + y = −2 and 2x + 3y = 14 →
  3. 3.2x + 3y = 8 and x + 4y = 24 →
  4. 4.3x − 2y = 20 and 3x − 5y = 14 →
  5. 5.4x + y = −24 and x + y = −3 →
  6. 6.4x − y = 17 and 2x + 6y = 28 →
  7. 7.6x + y = 25 and 4x + 3y = 19 →
  8. 8.6x + 7y = 2 and 7x + 6y = 11 →
  9. 9.5x − 2y = 31 and 5x − 3y = 29 →
  10. 10.6x + 4y = 8 and 4x + 6y = 2 →
  11. 11.5x − y = 4 and 5x + 5y = 40 →
  12. 12.3x − 4y = −23 and 2x − y = −2 →
  13. 13.3x + 2y = 24 and 2x + 3y = 31 →
  14. 14.2x + 6y = −68 and 6x + 2y = −60 →
  15. 15.6x − 2y = 34 and 3x + 6y = −39 →
  16. 16.3x + 8y = 49 and 8x + 3y = 39 →
  17. 17.3x + 6y = 54 and 6x + 6y = 78 →
  18. 18.3x + 3y = −15 and x + 2y = −2 →
  19. 19.6x + 9y = 24 and 9x + 6y = 21 →
  20. 20.x − y = 9 and 3x + 4y = −8 →
  21. 21.2x + 6y = 58 and 6x + 2y = 30 →
  22. 22.3x + 2y = 25 and 2x + 3y = 30 →
  23. 23.2x − 4y = 24 and 6x + 2y = 16 →
  24. 24.x + 3y = 20 and 2x + 4y = 22 →
  25. 25.2x + 5y = 29 and 3x − y = 1 →
  26. 26.7x + 2y = 37 and 2x + 7y = −28 →
  27. 27.3x + 5y = 24 and 2x − y = −10 →
  28. 28.3x − 6y = 0 and 6x + 2y = 56 →
  29. 29.6x + 9y = 114 and 9x + 6y = 111 →
  30. 30.5x + 3y = 59 and x − 6y = −41 →
  31. 31.9x + 5y = 38 and 5x + 9y = 46 →
  32. 32.x + 3y = 18 and x + 6y = 39 →
  33. 33.3x + 4y = 44 and 2x + y = 16 →
  34. 34.x + 5y = 7 and 5x + y = −37 →
  35. 35.x + 2y = −17 and 2x + y = −7 →
  36. 36.9x + 4y = 7 and 4x + 9y = 32 →
  37. 37.3x + 8y = 30 and 8x + 3y = −30 →
  38. 38.2x + 6y = 20 and 6x + 2y = 44 →
  39. 39.2x + 2y = −32 and 3x − 4y = 15 →
  40. 40.6x − 5y = 53 and 5x + 4y = 36 →

Answer key

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

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