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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 133 · 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 + y = 12 and 2x − 3y = −21 →
  2. 2.7x + 6y = 20 and 6x + 7y = 19 →
  3. 3.9x + 6y = 24 and 6x + 9y = 21 →
  4. 4.7x + 5y = 37 and 5x + 7y = 47 →
  5. 5.4x + y = 37 and x + 4y = 13 →
  6. 6.x + 6y = 45 and x + 4y = 29 →
  7. 7.2x + 6y = 68 and 6x + 2y = 60 →
  8. 8.x − 6y = −24 and x + 6y = 36 →
  9. 9.9x + 2y = −47 and 2x + 9y = 58 →
  10. 10.x − 4y = −9 and 3x − 2y = 3 →
  11. 11.x + y = 12 and 4x + y = 30 →
  12. 12.2x + 2y = 26 and 3x − y = 3 →
  13. 13.5x − y = −35 and x − 2y = 2 →
  14. 14.3x − 4y = −9 and 5x − 5y = 0 →
  15. 15.3x + 2y = −16 and 3x + 4y = −26 →
  16. 16.9x + y = −17 and x + 9y = −73 →
  17. 17.2x + 4y = −4 and 4x + 2y = −14 →
  18. 18.2x + 3y = 27 and 3x + 2y = 28 →
  19. 19.6x + 6y = −48 and 5x − 6y = 15 →
  20. 20.3x + 2y = 6 and 2x + 3y = 14 →
  21. 21.7x + 2y = −10 and 2x + 7y = 10 →
  22. 22.5x + y = 28 and 5x + 5y = 40 →
  23. 23.9x + 8y = 14 and 8x + 9y = 20 →
  24. 24.4x + 8y = 92 and 8x + 4y = 88 →
  25. 25.8x + 9y = 129 and 9x + 8y = 126 →
  26. 26.x + 4y = −9 and 4x + y = 24 →
  27. 27.4x + 8y = 100 and 8x + 4y = 104 →
  28. 28.5x + 4y = 14 and 4x + 5y = 4 →
  29. 29.2x + 2y = −2 and 3x − 2y = −8 →
  30. 30.5x + 5y = 60 and 4x − 6y = −42 →
  31. 31.6x + 3y = −75 and 3x + 6y = −78 →
  32. 32.5x + 7y = 54 and 7x + 5y = 42 →
  33. 33.4x + 6y = 58 and 2x + 6y = 56 →
  34. 34.6x + 5y = 13 and 3x − y = 10 →
  35. 35.x − 3y = 24 and 3x − 3y = 36 →
  36. 36.9x + 3y = 75 and 3x + 9y = 57 →
  37. 37.3x − 5y = −16 and x − y = 0 →
  38. 38.x + 2y = 7 and 2x + y = −1 →
  39. 39.3x − 2y = −7 and x + 6y = −49 →
  40. 40.2x + 5y = −11 and 2x + 4y = −6 →

Answer key

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

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