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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 748 · 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. 1.8x + 5y = 27 and 5x + 8y = 12 →
  2. 2.5x + y = 33 and 2x + 5y = 4 →
  3. 3.3x − 3y = −36 and 5x − 2y = −45 →
  4. 4.4x + 4y = 4 and 5x + 3y = −9 →
  5. 5.9x + 8y = 52 and 8x + 9y = 50 →
  6. 6.2x + 3y = 2 and 3x + 2y = 8 →
  7. 7.2x + 5y = 55 and 2x − y = 1 →
  8. 8.6x − 3y = −30 and 2x + 2y = 8 →
  9. 9.x − 4y = 10 and 4x + 5y = 19 →
  10. 10.x − 6y = −44 and 6x − 3y = 0 →
  11. 11.5x − 5y = −10 and 3x + 2y = 34 →
  12. 12.4x − y = 6 and x + 3y = 21 →
  13. 13.2x + y = −3 and x + 2y = −3 →
  14. 14.9x + 8y = 80 and 8x + 9y = 73 →
  15. 15.2x + 8y = 72 and 8x + 2y = 48 →
  16. 16.6x + 3y = −69 and 3x + 6y = −57 →
  17. 17.5x + y = 31 and x + 5y = 11 →
  18. 18.6x − y = 8 and 5x + 3y = 22 →
  19. 19.9x + 2y = 67 and 2x + 9y = 32 →
  20. 20.2x + 3y = 26 and 3x + 2y = 24 →
  21. 21.5x − 5y = 45 and 4x − 2y = 28 →
  22. 22.x + 3y = 29 and 3x − 4y = −17 →
  23. 23.5x + 3y = 36 and 3x + 5y = 12 →
  24. 24.6x − 4y = 42 and 2x − 6y = 0 →
  25. 25.2x + y = 22 and x + 4y = 39 →
  26. 26.x + 3y = 8 and 3x + 2y = −11 →
  27. 27.2x + 5y = −36 and 6x − 3y = 0 →
  28. 28.x + 3y = −6 and 5x + 4y = 3 →
  29. 29.5x − 2y = 20 and 5x + 6y = 60 →
  30. 30.6x − 3y = 30 and x + 4y = −4 →
  31. 31.2x − 5y = −22 and x + 5y = 4 →
  32. 32.3x − 2y = −28 and 4x − 6y = −44 →
  33. 33.5x − 4y = 16 and 2x + 3y = 34 →
  34. 34.3x + 6y = 21 and 4x + 4y = 20 →
  35. 35.x + 7y = 17 and 7x + y = 23 →
  36. 36.4x + 7y = −77 and 7x + 4y = −77 →
  37. 37.4x − 4y = 24 and 4x + 5y = 6 →
  38. 38.9x + 4y = 38 and 4x + 9y = −12 →
  39. 39.2x + y = 5 and x − 3y = 27 →
  40. 40.x − y = 7 and 2x + 4y = 26 →

Answer key

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

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