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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 7 · 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 + 3y = 31 and 3x + 4y = 39 →
  2. 2.3x + 4y = −11 and 4x + 3y = −10 →
  3. 3.4x − 4y = 52 and 5x + 2y = 23 →
  4. 4.x − y = −1 and 6x + y = 8 →
  5. 5.5x − 3y = −43 and x + 2y = 7 →
  6. 6.3x + 2y = 2 and 4x + 5y = 19 →
  7. 7.4x − y = 9 and 6x − 6y = 0 →
  8. 8.2x + 6y = 2 and 6x + 2y = −42 →
  9. 9.x + 6y = −26 and 2x + 4y = −20 →
  10. 10.5x + 4y = −26 and 3x + y = −10 →
  11. 11.x + 6y = −39 and 6x + 5y = −17 →
  12. 12.3x + 6y = −63 and 2x + 6y = −54 →
  13. 13.3x − 3y = −9 and 2x + y = −18 →
  14. 14.x + 2y = −15 and x − y = 12 →
  15. 15.2x + 4y = −54 and 4x + 2y = −54 →
  16. 16.2x + 4y = 12 and 4x + 2y = −12 →
  17. 17.2x + y = 12 and x + 2y = 15 →
  18. 18.2x + 4y = 6 and 4x + 2y = −18 →
  19. 19.3x + 4y = 20 and 3x − 2y = 8 →
  20. 20.4x + y = −1 and 4x + 2y = −10 →
  21. 21.5x + y = 48 and 3x + 6y = 72 →
  22. 22.2x + 7y = −20 and 7x + 2y = −25 →
  23. 23.x + 5y = −8 and 5x + y = 8 →
  24. 24.2x + 6y = 42 and 3x − 6y = −27 →
  25. 25.8x + 5y = −24 and 5x + 8y = 24 →
  26. 26.3x + 6y = −30 and 3x + 5y = −29 →
  27. 27.3x + 4y = 17 and 5x + 2y = 19 →
  28. 28.6x + 2y = −44 and x − 6y = −39 →
  29. 29.6x + 4y = 36 and 6x − 2y = 0 →
  30. 30.6x + 5y = 54 and 5x + 6y = 56 →
  31. 31.4x − 6y = 74 and 3x + y = 17 →
  32. 32.5x − 5y = 15 and 3x + 3y = 15 →
  33. 33.2x + 8y = 20 and 8x + 2y = 20 →
  34. 34.5x + y = −24 and 2x + 6y = −60 →
  35. 35.2x + y = 5 and x + 2y = −11 →
  36. 36.8x + 6y = 22 and 6x + 8y = 20 →
  37. 37.3x + 5y = 56 and 5x + 3y = 56 →
  38. 38.x − 6y = −23 and 5x + 2y = 45 →
  39. 39.4x + 2y = 36 and 5x − 4y = 32 →
  40. 40.8x + 7y = 45 and 7x + 8y = 45 →

Answer key

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

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