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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 91 · 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. 1.2x + 4y = 42 and x + 3y = 28 →
  2. 2.x + 9y = 52 and 9x + y = −12 →
  3. 3.2x + 4y = 34 and 4x + 2y = 20 →
  4. 4.8x + 3y = 17 and 3x + 8y = 27 →
  5. 5.5x + 5y = 20 and 6x − 6y = 60 →
  6. 6.3x − 4y = −1 and x − y = 0 →
  7. 7.5x + 8y = −69 and 8x + 5y = −87 →
  8. 8.x − 4y = −33 and 2x + 3y = 22 →
  9. 9.2x + 2y = 6 and 6x + 2y = −14 →
  10. 10.9x + y = −37 and x + 9y = 67 →
  11. 11.2x + 2y = 14 and 3x + 6y = 30 →
  12. 12.3x + 4y = 21 and 6x + 2y = 6 →
  13. 13.8x + 3y = −40 and 3x + 8y = 40 →
  14. 14.2x + 4y = −38 and 4x + 6y = −64 →
  15. 15.5x + y = −30 and 5x − 2y = −45 →
  16. 16.2x + 3y = 11 and 6x + 3y = 15 →
  17. 17.2x − y = −12 and 3x − y = −16 →
  18. 18.3x + 9y = −66 and 9x + 3y = 18 →
  19. 19.2x − 6y = −4 and x + 3y = 4 →
  20. 20.6x + 6y = 54 and 3x − 5y = 11 →
  21. 21.x + 2y = 13 and 3x + 5y = 32 →
  22. 22.6x + 4y = 12 and 5x + y = 24 →
  23. 23.7x + 6y = 62 and 6x + 7y = 55 →
  24. 24.5x + 9y = −14 and 9x + 5y = −14 →
  25. 25.3x + 6y = −57 and 6x + 3y = −33 →
  26. 26.3x − 5y = −1 and x − 6y = 4 →
  27. 27.3x − 2y = 15 and x + 2y = 13 →
  28. 28.2x + 3y = 22 and 3x + 2y = 28 →
  29. 29.6x − 4y = −30 and 6x + 3y = 12 →
  30. 30.3x + y = 0 and x − 2y = 14 →
  31. 31.3x + 4y = 11 and 4x + 3y = 24 →
  32. 32.2x + y = −17 and 5x + 3y = −42 →
  33. 33.4x + 4y = 12 and 5x + 2y = −12 →
  34. 34.2x − y = −1 and 5x + 5y = 20 →
  35. 35.6x − 6y = 36 and x + y = −8 →
  36. 36.3x + 5y = 23 and 5x + 3y = 17 →
  37. 37.6x + y = 60 and 3x + 6y = 63 →
  38. 38.2x + 2y = 20 and 4x − y = 25 →
  39. 39.9x + 8y = −89 and 8x + 9y = −81 →
  40. 40.4x + 8y = −36 and 8x + 4y = 36 →

Answer key

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

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