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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 397 · 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. 1.9x + 4y = 96 and 4x + 9y = 86 →
  2. 2.2x − 3y = 9 and 6x + 2y = 16 →
  3. 3.x + 6y = −40 and 6x − y = 56 →
  4. 4.2x + 5y = 6 and 2x − 2y = −8 →
  5. 5.5x + 2y = −57 and 2x − 3y = 0 →
  6. 6.3x + y = −33 and 5x − 5y = 5 →
  7. 7.4x + 9y = 47 and 9x + 4y = −8 →
  8. 8.x + 7y = −52 and 7x + y = −28 →
  9. 9.2x − 6y = 2 and 2x + 4y = 12 →
  10. 10.6x + y = 21 and x + 6y = 21 →
  11. 11.2x + 2y = −24 and 3x + 4y = −45 →
  12. 12.3x + y = 10 and 2x + y = 6 →
  13. 13.2x + 4y = 16 and 2x + 6y = 26 →
  14. 14.x − 2y = 3 and 4x + 4y = 36 →
  15. 15.3x − y = −14 and 6x − y = −26 →
  16. 16.4x + 4y = 20 and 2x − 3y = −10 →
  17. 17.3x + 4y = 31 and 6x + 3y = 27 →
  18. 18.5x + y = −18 and 6x + y = −23 →
  19. 19.5x − 6y = 7 and 6x − 5y = 15 →
  20. 20.3x + 5y = 21 and 6x + y = −39 →
  21. 21.x + 6y = 15 and 3x + 4y = 31 →
  22. 22.2x + 6y = 2 and 4x + 3y = −5 →
  23. 23.4x + 4y = −24 and 5x + 2y = −33 →
  24. 24.7x + 8y = 113 and 8x + 7y = 112 →
  25. 25.4x + 3y = −18 and 6x + 6y = −18 →
  26. 26.4x + 2y = −12 and 2x − 3y = −14 →
  27. 27.5x + 2y = 22 and 4x + 5y = 38 →
  28. 28.7x + 4y = 16 and 4x + 7y = −5 →
  29. 29.3x + 2y = 5 and 4x + 5y = −12 →
  30. 30.3x + y = 5 and 5x − y = 3 →
  31. 31.3x + 9y = −81 and 9x + 3y = −99 →
  32. 32.4x + 8y = −60 and 8x + 4y = −84 →
  33. 33.7x + 9y = 58 and 9x + 7y = 38 →
  34. 34.x − y = −5 and 3x + y = −7 →
  35. 35.x + 2y = −16 and 2x + y = −5 →
  36. 36.3x + 6y = 3 and 6x + 3y = 24 →
  37. 37.2x + y = 1 and 4x − 6y = 42 →
  38. 38.4x + 7y = 87 and 7x + 4y = 78 →
  39. 39.x − 4y = 5 and x + 3y = −2 →
  40. 40.2x + 5y = −23 and 5x − 5y = −5 →

Answer key

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

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