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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 669 · 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. 1.7x + 5y = 37 and 5x + 7y = 47 →
  2. 2.x + 2y = 5 and 2x + y = 4 →
  3. 3.5x − 2y = 0 and 5x − 5y = 15 →
  4. 4.2x + 5y = 57 and 2x + 4y = 48 →
  5. 5.6x + 5y = 18 and 6x − 5y = −42 →
  6. 6.6x + 3y = 24 and 3x + 6y = 21 →
  7. 7.2x + 6y = 56 and 6x + 2y = 56 →
  8. 8.x − 5y = 41 and 4x + y = −25 →
  9. 9.4x + y = 27 and 4x − 2y = 18 →
  10. 10.3x + 4y = −31 and 6x + 6y = −48 →
  11. 11.6x + 5y = 4 and 3x + 2y = 4 →
  12. 12.4x + 4y = −40 and 3x + y = −20 →
  13. 13.x − 3y = 15 and 2x + 6y = −18 →
  14. 14.3x − 2y = 14 and 2x + 2y = 16 →
  15. 15.6x − 5y = 52 and 2x − 3y = 28 →
  16. 16.4x + 6y = 90 and 2x + 4y = 54 →
  17. 17.5x − 4y = −23 and 3x + y = 10 →
  18. 18.7x + 3y = 13 and 3x + 7y = 17 →
  19. 19.2x + 3y = 15 and 3x + 2y = 20 →
  20. 20.6x + 5y = −4 and 3x + 3y = −3 →
  21. 21.4x − 5y = −17 and 5x − 2y = 17 →
  22. 22.x − 3y = −6 and 6x − y = 32 →
  23. 23.3x + 6y = 63 and 6x + 3y = 63 →
  24. 24.x − 2y = −10 and 5x + 2y = 58 →
  25. 25.5x + 3y = 34 and x + 5y = 20 →
  26. 26.3x + 2y = 37 and 5x + 5y = 75 →
  27. 27.5x + 7y = 70 and 7x + 5y = 74 →
  28. 28.7x + 8y = −35 and 8x + 7y = −25 →
  29. 29.x + 8y = −34 and 8x + y = 43 →
  30. 30.7x + y = 49 and x + 7y = 55 →
  31. 31.3x + 4y = 40 and 4x + 3y = 37 →
  32. 32.5x + 2y = 41 and 4x + 2y = 34 →
  33. 33.9x + 5y = 19 and 5x + 9y = 23 →
  34. 34.7x + 8y = 114 and 8x + 7y = 111 →
  35. 35.3x + 4y = −18 and x + 3y = −21 →
  36. 36.x + 8y = 63 and 8x + y = 63 →
  37. 37.5x + 3y = 37 and 3x + 5y = 19 →
  38. 38.5x + 7y = −31 and 7x + 5y = −5 →
  39. 39.4x + 9y = 25 and 9x + 4y = 40 →
  40. 40.5x + 4y = 7 and 5x − 4y = −17 →

Answer key

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

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