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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 190 · 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. 1.6x + 6y = 48 and x + 3y = 22 →
  2. 2.4x + 6y = −6 and x + 6y = −24 →
  3. 3.5x + 5y = −70 and 6x + 5y = −79 →
  4. 4.3x − y = −11 and 4x + 6y = −44 →
  5. 5.6x + 4y = −80 and 3x + 4y = −56 →
  6. 6.4x + 5y = 49 and 5x + 4y = 50 →
  7. 7.2x + y = 6 and 4x + 3y = 6 →
  8. 8.2x + 2y = 16 and x − 5y = −28 →
  9. 9.8x + 5y = 21 and 5x + 8y = 18 →
  10. 10.x + 2y = 5 and 2x + y = 7 →
  11. 11.2x + 2y = 12 and 4x + 5y = 26 →
  12. 12.x + 4y = 12 and 2x + 3y = 19 →
  13. 13.x + 3y = 31 and 4x + 3y = 52 →
  14. 14.x + 5y = −17 and 3x + 3y = 9 →
  15. 15.3x + 9y = 3 and 9x + 3y = 33 →
  16. 16.3x + 9y = −75 and 9x + 3y = −9 →
  17. 17.2x − 3y = 33 and 2x + 3y = 3 →
  18. 18.8x + y = 26 and x + 8y = −44 →
  19. 19.2x + 2y = 16 and 6x + y = 23 →
  20. 20.4x − 2y = 22 and 3x + 6y = −51 →
  21. 21.9x + 3y = 105 and 3x + 9y = 99 →
  22. 22.4x + y = 38 and x + y = 11 →
  23. 23.x + 4y = 1 and 4x + y = 34 →
  24. 24.x − 2y = −1 and 2x + 5y = 7 →
  25. 25.4x + y = 9 and 3x − y = 5 →
  26. 26.x + 4y = 15 and x + 2y = 9 →
  27. 27.8x + 5y = 29 and 5x + 8y = −16 →
  28. 28.3x − 2y = −1 and 4x + 6y = 68 →
  29. 29.x + 8y = −55 and 8x + y = 1 →
  30. 30.2x + 2y = 8 and 3x + 2y = 17 →
  31. 31.6x + y = 8 and 4x + 5y = −12 →
  32. 32.4x − y = 12 and 2x − y = 8 →
  33. 33.5x + 3y = 39 and x + y = 7 →
  34. 34.x + 6y = −36 and x − y = −1 →
  35. 35.5x + 4y = 13 and 5x + 2y = 29 →
  36. 36.5x + 6y = 75 and 6x + 5y = 79 →
  37. 37.9x + 8y = 127 and 8x + 9y = 128 →
  38. 38.2x − 6y = 36 and 4x + 2y = 16 →
  39. 39.4x + 6y = −66 and 6x + 4y = −54 →
  40. 40.x − 3y = 13 and 3x + 4y = −13 →

Answer key

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

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