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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 217 · 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 − y = 35 and 2x − 4y = 42 →
  2. 2.2x − 4y = −2 and 4x + 4y = 8 →
  3. 3.6x + 4y = 26 and 4x + 6y = 34 →
  4. 4.x + 4y = 33 and 4x + 3y = 54 →
  5. 5.3x + 5y = 16 and 5x + 6y = 8 →
  6. 6.2x + 5y = 21 and 5x + 2y = 21 →
  7. 7.6x + 4y = −64 and 4x + 6y = −66 →
  8. 8.5x + 9y = −7 and 9x + 5y = 21 →
  9. 9.3x + 2y = 10 and 2x + 3y = 0 →
  10. 10.2x + 2y = −14 and x + 2y = −11 →
  11. 11.5x + 9y = −28 and 9x + 5y = 28 →
  12. 12.x + 8y = 55 and 8x + y = 62 →
  13. 13.6x + 5y = 48 and 5x + 6y = 51 →
  14. 14.4x + 4y = 44 and x − 6y = −52 →
  15. 15.8x + 6y = 30 and 6x + 8y = 26 →
  16. 16.2x + y = 8 and 4x − 6y = −16 →
  17. 17.2x + 4y = 54 and 4x + 4y = 72 →
  18. 18.5x + 6y = 29 and 6x + 5y = 26 →
  19. 19.x + 2y = −3 and x − 2y = 9 →
  20. 20.x + 3y = −18 and x − 5y = 46 →
  21. 21.2x + 7y = 53 and 7x + 2y = 28 →
  22. 22.x − 2y = −9 and 6x + 5y = 82 →
  23. 23.x + 8y = 58 and 8x + y = 23 →
  24. 24.5x − 2y = −14 and 6x − 4y = −20 →
  25. 25.2x + 5y = −8 and 5x + 2y = 1 →
  26. 26.4x + 4y = 0 and 6x − 2y = 16 →
  27. 27.8x + y = 41 and x + 8y = 76 →
  28. 28.7x + 4y = 3 and 4x + 7y = −36 →
  29. 29.5x + y = 42 and x + 5y = 18 →
  30. 30.6x − y = 33 and 4x − 5y = 9 →
  31. 31.2x − y = 11 and x + 4y = −17 →
  32. 32.x + 6y = 62 and 4x + 5y = 77 →
  33. 33.x + 6y = 33 and 3x + 2y = 19 →
  34. 34.4x + y = −8 and 3x − y = −20 →
  35. 35.x + 3y = 23 and 5x + y = 31 →
  36. 36.3x + 6y = 21 and 4x − 2y = −32 →
  37. 37.2x + 3y = 29 and 3x + 2y = 21 →
  38. 38.6x + y = 13 and 2x − 2y = 2 →
  39. 39.3x − 5y = 30 and 5x − 5y = 20 →
  40. 40.9x + 8y = 56 and 8x + 9y = 46 →

Answer key

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

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