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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 199 · 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. 1.5x + 4y = −13 and 6x − 6y = −102 →
  2. 2.x + 8y = −37 and 8x + y = −44 →
  3. 3.6x + y = 24 and 4x + y = 18 →
  4. 4.4x − 4y = −48 and 5x + 2y = −11 →
  5. 5.x + 4y = 9 and 4x + 2y = 22 →
  6. 6.2x − 2y = 6 and x + 4y = −2 →
  7. 7.7x + 3y = 35 and 3x + 7y = 55 →
  8. 8.2x + 5y = 3 and 5x + 2y = 39 →
  9. 9.5x + 2y = 32 and 4x − 5y = −14 →
  10. 10.3x + 5y = −30 and 6x − 3y = −21 →
  11. 11.3x + y = 22 and 6x − 3y = 39 →
  12. 12.2x + 6y = −12 and 4x + 3y = 12 →
  13. 13.7x + 4y = 23 and 4x + 7y = 32 →
  14. 14.x + 5y = 41 and 4x + 5y = 59 →
  15. 15.x + 2y = 13 and 2x + y = 8 →
  16. 16.x + 3y = 13 and 5x − y = 17 →
  17. 17.5x + 4y = 25 and 4x + 5y = 11 →
  18. 18.4x + 9y = −21 and 9x + 4y = −31 →
  19. 19.4x − 3y = 18 and 5x + 3y = 36 →
  20. 20.9x + 4y = 35 and 4x + 9y = −35 →
  21. 21.x + y = 11 and 4x − 4y = −28 →
  22. 22.x + y = 12 and 2x + 4y = 36 →
  23. 23.6x − 5y = 3 and x − y = 0 →
  24. 24.9x + 3y = 96 and 3x + 9y = 96 →
  25. 25.2x + y = 4 and x + 2y = 11 →
  26. 26.6x + 3y = 48 and x − 4y = −28 →
  27. 27.5x − 5y = 15 and 2x + 3y = −19 →
  28. 28.6x + 9y = −84 and 9x + 6y = −66 →
  29. 29.x + 5y = 19 and 6x − 6y = 6 →
  30. 30.3x + 5y = 54 and 6x + y = 54 →
  31. 31.8x + 5y = 68 and 5x + 8y = 62 →
  32. 32.x + 4y = −28 and 3x + y = 4 →
  33. 33.6x + y = 17 and 5x + 5y = 35 →
  34. 34.x − 6y = −31 and 4x + 4y = 44 →
  35. 35.2x + 5y = −8 and 5x + 2y = 22 →
  36. 36.3x − 3y = 18 and 2x + 5y = −37 →
  37. 37.3x + 3y = 9 and 3x + 5y = 19 →
  38. 38.4x + 2y = −22 and 2x − y = 3 →
  39. 39.3x + 8y = 46 and 8x + 3y = 31 →
  40. 40.6x − y = −54 and 4x + 5y = −2 →

Answer key

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

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