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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 929 · 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 − 2y = −22 and 5x − 3y = −34 →
  2. 2.x + 6y = −11 and 4x − 2y = 34 →
  3. 3.6x + 4y = 40 and 6x − 4y = 8 →
  4. 4.7x + 6y = 1 and 6x + 7y = −1 →
  5. 5.5x + 4y = 12 and 5x + 3y = 14 →
  6. 6.x + 6y = −22 and 6x + y = 8 →
  7. 7.7x + 9y = 74 and 9x + 7y = 86 →
  8. 8.5x − y = −41 and x + 3y = −5 →
  9. 9.2x − 2y = −12 and x + 5y = 0 →
  10. 10.4x + y = 37 and 6x + y = 51 →
  11. 11.3x + 2y = −14 and x − 2y = −2 →
  12. 12.6x + 2y = −18 and 2x − 5y = 11 →
  13. 13.2x + 5y = −24 and 6x + 2y = 32 →
  14. 14.x + 3y = 8 and 4x + y = −12 →
  15. 15.6x + 3y = −24 and 2x + 5y = −32 →
  16. 16.4x + 2y = 22 and 3x + 6y = 21 →
  17. 17.6x + 2y = 16 and 2x − y = −3 →
  18. 18.9x + 7y = 73 and 7x + 9y = 71 →
  19. 19.x + 8y = 63 and 8x + y = 63 →
  20. 20.7x + 3y = 32 and 3x + 7y = 48 →
  21. 21.x − 2y = 7 and 2x − y = 8 →
  22. 22.x − 5y = 6 and 4x − 3y = −27 →
  23. 23.6x + y = 52 and 5x + 5y = 60 →
  24. 24.3x + 2y = −6 and 4x − 4y = −68 →
  25. 25.6x − 2y = 26 and 6x + y = 41 →
  26. 26.7x + 9y = 53 and 9x + 7y = 59 →
  27. 27.6x − 2y = −56 and 5x + y = −36 →
  28. 28.x − 6y = −14 and 4x − 2y = −12 →
  29. 29.4x + 2y = 20 and 6x + y = 18 →
  30. 30.4x + 7y = 70 and 7x + 4y = 73 →
  31. 31.3x + 8y = 11 and 8x + 3y = 66 →
  32. 32.6x + 2y = −10 and 6x − y = 14 →
  33. 33.6x + y = 53 and 4x + 2y = 42 →
  34. 34.x + 5y = 18 and 5x − 4y = 3 →
  35. 35.2x − y = 11 and 5x + 6y = 53 →
  36. 36.2x + 6y = 32 and 4x + 5y = 36 →
  37. 37.3x + 9y = −12 and 9x + 3y = 60 →
  38. 38.x − 6y = −3 and 3x − 3y = 6 →
  39. 39.2x − 4y = −30 and x + y = 12 →
  40. 40.4x + 2y = 16 and x + 3y = 9 →

Answer key

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

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