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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 483 · 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 = 7 and 3x − y = −11 →
  2. 2.4x + 5y = 15 and 5x + 4y = 21 →
  3. 3.2x − 2y = 22 and 4x + y = 9 →
  4. 4.4x + 3y = 16 and 5x + 4y = 21 →
  5. 5.5x − 6y = 78 and 5x + 5y = −10 →
  6. 6.x + 5y = −17 and 2x + 6y = −18 →
  7. 7.3x + 3y = 0 and x + 5y = −4 →
  8. 8.7x + 5y = 5 and 5x + 7y = 31 →
  9. 9.9x + 3y = 57 and 3x + 9y = 27 →
  10. 10.x + 7y = 51 and 7x + y = −27 →
  11. 11.5x + 2y = −33 and 3x + y = −20 →
  12. 12.5x + 6y = 14 and 6x + 5y = 19 →
  13. 13.6x − 5y = −77 and 4x − 4y = −56 →
  14. 14.5x − y = 29 and 5x + y = 31 →
  15. 15.2x + 8y = 74 and 8x + 2y = 26 →
  16. 16.3x + 3y = 39 and 3x − y = 19 →
  17. 17.3x + 6y = −24 and x − 4y = 22 →
  18. 18.6x + 3y = 51 and 5x + 4y = 56 →
  19. 19.5x + 9y = 102 and 9x + 5y = 94 →
  20. 20.5x + y = −37 and x + 5y = −17 →
  21. 21.5x + 3y = 13 and x − 6y = −4 →
  22. 22.4x + 5y = 23 and 5x + 4y = 22 →
  23. 23.4x + 6y = 60 and 3x − 6y = −18 →
  24. 24.2x + 2y = −14 and 5x + 3y = −39 →
  25. 25.4x − 4y = 8 and 3x + 2y = −39 →
  26. 26.5x + 2y = 30 and 2x + 3y = 1 →
  27. 27.6x − 5y = −77 and x + 3y = 14 →
  28. 28.7x + 9y = −40 and 9x + 7y = −56 →
  29. 29.x + 3y = −12 and 4x + 2y = −18 →
  30. 30.2x + 2y = 8 and 4x − 5y = 7 →
  31. 31.8x + 2y = 54 and 2x + 8y = 6 →
  32. 32.x + 3y = −4 and 3x + 2y = 2 →
  33. 33.2x + 2y = −12 and x − 4y = −21 →
  34. 34.2x + 5y = −47 and 5x − 6y = 49 →
  35. 35.3x − 3y = 3 and x + 3y = −27 →
  36. 36.4x + 3y = 7 and 4x − y = 3 →
  37. 37.2x − 2y = −8 and 3x − 2y = −3 →
  38. 38.3x + 8y = 58 and 8x + 3y = 8 →
  39. 39.5x + y = 32 and 2x + y = 17 →
  40. 40.2x + 6y = −20 and x + 6y = −25 →

Answer key

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

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