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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 744 · 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.x − 3y = 7 and 4x − 6y = 4 →
  2. 2.2x + 6y = −6 and 6x + 2y = −50 →
  3. 3.x + 8y = 53 and 8x + y = −17 →
  4. 4.2x + 4y = 10 and 4x + 2y = −4 →
  5. 5.x + y = 8 and 2x + 4y = 20 →
  6. 6.4x + 7y = −50 and 7x + 4y = −38 →
  7. 7.x + y = 11 and 3x − 2y = 23 →
  8. 8.3x + 4y = 17 and x + 5y = 13 →
  9. 9.3x + 4y = −63 and 4x + 3y = −63 →
  10. 10.6x + 2y = 32 and 5x + y = 26 →
  11. 11.6x + 2y = −6 and x − y = −5 →
  12. 12.x + 2y = 12 and 2x + y = 18 →
  13. 13.5x + 3y = 16 and 3x + 5y = 0 →
  14. 14.2x + y = −9 and x + 2y = 0 →
  15. 15.6x + 5y = −24 and 5x + 6y = −9 →
  16. 16.6x − 6y = −18 and 2x + 5y = 8 →
  17. 17.3x + 7y = 10 and 7x + 3y = −30 →
  18. 18.3x − 5y = 6 and 3x + y = 24 →
  19. 19.5x + 3y = 14 and 4x + 4y = 24 →
  20. 20.x + 2y = 11 and 2x + y = 10 →
  21. 21.3x + 2y = −14 and 3x − 4y = −8 →
  22. 22.2x + 5y = 44 and 2x + 2y = 20 →
  23. 23.5x + y = 39 and x + 5y = 27 →
  24. 24.3x + 2y = −11 and 6x − 5y = 41 →
  25. 25.6x + 4y = 0 and x + 6y = −16 →
  26. 26.6x + 2y = 4 and 5x + 6y = −1 →
  27. 27.5x + y = −16 and x + 4y = 31 →
  28. 28.3x + 5y = 51 and x + 2y = 20 →
  29. 29.4x − 2y = 30 and 6x + 6y = 0 →
  30. 30.9x + y = −8 and x + 9y = 8 →
  31. 31.6x + 3y = −48 and 5x + 3y = −39 →
  32. 32.5x + 2y = 42 and 5x + y = 41 →
  33. 33.2x + 4y = −6 and 3x + 2y = −17 →
  34. 34.x + 6y = −26 and 5x − 6y = 50 →
  35. 35.6x + 6y = 30 and x + 4y = 14 →
  36. 36.2x − 2y = −20 and 3x + 2y = −15 →
  37. 37.x + 3y = 12 and 3x − y = −14 →
  38. 38.4x + 5y = 63 and 2x + 5y = 49 →
  39. 39.x + 6y = −3 and 3x − 2y = −29 →
  40. 40.6x − 6y = −6 and 3x − 4y = −9 →

Answer key

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

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