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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 185 · 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 + 5y = −33 and 6x + 6y = −30 →
  2. 2.4x − y = 22 and x + 6y = 43 →
  3. 3.4x + 3y = −40 and 3x − y = −17 →
  4. 4.8x + 3y = −44 and 3x + 8y = 11 →
  5. 5.5x − y = −48 and x + 6y = 9 →
  6. 6.2x + 4y = −16 and 2x + 5y = −22 →
  7. 7.3x + 2y = 17 and 4x − 5y = −8 →
  8. 8.2x + 3y = 27 and 3x + 2y = 23 →
  9. 9.6x − 6y = −42 and 3x + 6y = −12 →
  10. 10.7x + 3y = 29 and 3x + 7y = −39 →
  11. 11.3x + 2y = −25 and 2x + 3y = −25 →
  12. 12.8x + y = 41 and x + 8y = −50 →
  13. 13.6x + 3y = 24 and 3x + 6y = 21 →
  14. 14.3x + 8y = 85 and 8x + 3y = 80 →
  15. 15.6x + 6y = −48 and 4x − 4y = −24 →
  16. 16.2x + 3y = 25 and 3x + 2y = 15 →
  17. 17.6x + y = 38 and x + 2y = 10 →
  18. 18.6x + 4y = −14 and 4x + 5y = −7 →
  19. 19.3x + 2y = −7 and x − y = 6 →
  20. 20.2x − 2y = 14 and x − 4y = 22 →
  21. 21.6x + 4y = 56 and x − 2y = −4 →
  22. 22.x + 2y = −5 and 3x + 3y = −6 →
  23. 23.6x + 3y = 9 and 3x + 6y = 45 →
  24. 24.4x + 5y = 72 and 5x + 4y = 72 →
  25. 25.6x + y = −32 and x + 3y = −11 →
  26. 26.6x + 7y = 53 and 7x + 6y = 51 →
  27. 27.5x + y = 44 and 4x − 2y = 10 →
  28. 28.3x + 9y = 30 and 9x + 3y = 18 →
  29. 29.2x + 5y = 38 and x + y = 7 →
  30. 30.5x − 5y = 65 and 2x + 6y = −38 →
  31. 31.5x + 2y = −44 and 2x + 4y = −24 →
  32. 32.x + 3y = 22 and 2x − 4y = −36 →
  33. 33.9x + 6y = 87 and 6x + 9y = 78 →
  34. 34.3x − 2y = −11 and 4x + 4y = 32 →
  35. 35.6x + 3y = 21 and 3x + 6y = −3 →
  36. 36.3x + 2y = 0 and 4x + y = −5 →
  37. 37.9x + 5y = 39 and 5x + 9y = 3 →
  38. 38.x + 2y = −12 and x + y = −9 →
  39. 39.2x + 3y = −30 and 3x + 2y = −30 →
  40. 40.6x + y = 22 and 2x − y = 2 →

Answer key

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

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