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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 373 · 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 + y = 42 and 5x − 2y = 36 →
  2. 2.9x + y = −18 and x + 9y = 78 →
  3. 3.5x − y = 31 and x + 4y = 23 →
  4. 4.7x + y = −60 and x + 7y = 12 →
  5. 5.4x + 2y = 18 and 5x − 5y = 30 →
  6. 6.2x + 4y = −24 and 4x + 2y = −24 →
  7. 7.5x + 5y = 55 and 5x + 2y = 49 →
  8. 8.2x + 6y = 44 and 3x − 4y = −12 →
  9. 9.2x + 9y = 72 and 9x + 2y = 93 →
  10. 10.9x + y = −44 and x + 9y = −76 →
  11. 11.2x − 5y = −43 and 5x − 6y = −62 →
  12. 12.2x + 6y = 14 and 6x + 2y = 10 →
  13. 13.9x + 2y = −24 and 2x + 9y = −31 →
  14. 14.5x + 7y = 28 and 7x + 5y = 44 →
  15. 15.8x + 3y = 27 and 3x + 8y = 17 →
  16. 16.4x + 3y = 14 and 2x − 2y = 14 →
  17. 17.3x − 3y = 0 and 3x − 6y = −6 →
  18. 18.5x + y = 48 and 4x + 2y = 48 →
  19. 19.5x − 3y = 17 and 4x + 6y = 22 →
  20. 20.x + 5y = −28 and 5x − 6y = 46 →
  21. 21.6x − 4y = 8 and 4x + 5y = 36 →
  22. 22.x + 4y = −2 and 5x + 4y = 22 →
  23. 23.x + 6y = 57 and 2x − y = 10 →
  24. 24.6x + 6y = 0 and 4x − y = 30 →
  25. 25.6x + 5y = −28 and 5x + 6y = −38 →
  26. 26.7x + y = 63 and x + 7y = 57 →
  27. 27.5x + 5y = −5 and 2x − 2y = −26 →
  28. 28.5x − 5y = 80 and x + 5y = −26 →
  29. 29.x + 4y = −7 and 5x + y = 22 →
  30. 30.3x − 4y = −32 and 2x + 2y = −12 →
  31. 31.x + 6y = 15 and x − y = 8 →
  32. 32.4x − 4y = −28 and 6x + 5y = 46 →
  33. 33.x + 4y = 16 and 5x + y = 23 →
  34. 34.9x + 3y = −3 and 3x + 9y = −33 →
  35. 35.5x + 5y = 45 and x + 4y = 21 →
  36. 36.9x + 3y = 45 and 3x + 9y = 63 →
  37. 37.x + 4y = 12 and 6x + 5y = −4 →
  38. 38.2x − y = 12 and 2x + 6y = −2 →
  39. 39.6x + 3y = 51 and 2x + 5y = 45 →
  40. 40.5x − 6y = 50 and 6x − 2y = 34 →

Answer key

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

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