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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 83 · 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 + 3y = 24 and 4x + 3y = 42 →
  2. 2.6x + 2y = 64 and 2x + 6y = 48 →
  3. 3.4x + 5y = 7 and 4x − y = −11 →
  4. 4.6x − 2y = 2 and 6x + 2y = 34 →
  5. 5.2x + y = 9 and 3x + y = 16 →
  6. 6.2x − 2y = −18 and 6x + 5y = −10 →
  7. 7.3x + 2y = 25 and 6x + 2y = 40 →
  8. 8.8x + 2y = −58 and 2x + 8y = 8 →
  9. 9.2x + 4y = 26 and 4x + 2y = 28 →
  10. 10.2x + y = 19 and x + 2y = 11 →
  11. 11.3x − 3y = −12 and 6x + 4y = −64 →
  12. 12.3x + 9y = 45 and 9x + 3y = 63 →
  13. 13.x + 4y = 19 and 2x + 6y = 32 →
  14. 14.2x + 5y = 8 and x + 3y = 5 →
  15. 15.3x + 8y = 11 and 8x + 3y = 11 →
  16. 16.x + 4y = 25 and 3x + 3y = 21 →
  17. 17.6x − 2y = −24 and 3x + 3y = 12 →
  18. 18.5x + 3y = 69 and 4x + 5y = 76 →
  19. 19.6x + 2y = −50 and 2x + 6y = −6 →
  20. 20.6x + 3y = 33 and 6x − y = 21 →
  21. 21.4x + 9y = 81 and 9x + 4y = 101 →
  22. 22.3x − 2y = 17 and 5x + 6y = 19 →
  23. 23.6x − 3y = 18 and 3x + 4y = −2 →
  24. 24.5x + 2y = −7 and 3x + 6y = 15 →
  25. 25.6x + y = 47 and 6x + 6y = 72 →
  26. 26.5x − 6y = −16 and 2x + 3y = 26 →
  27. 27.4x + 2y = −32 and 5x + 2y = −38 →
  28. 28.7x + 4y = 48 and 4x + 7y = 18 →
  29. 29.3x + 5y = 12 and 3x + 3y = 0 →
  30. 30.3x − 4y = −26 and x + 2y = 8 →
  31. 31.5x + y = 6 and 2x + 6y = −48 →
  32. 32.x + 5y = −27 and 2x + 6y = −26 →
  33. 33.7x + 3y = 41 and 3x + 7y = −11 →
  34. 34.2x + 4y = 46 and 4x − y = 11 →
  35. 35.x + 5y = 17 and 6x + y = 15 →
  36. 36.4x + 3y = 13 and 2x + 2y = 8 →
  37. 37.2x + 2y = 16 and 3x − 6y = −21 →
  38. 38.6x − 2y = −28 and 5x + 5y = −50 →
  39. 39.2x + 2y = −20 and 5x − 5y = 40 →
  40. 40.x − 3y = 23 and x + 2y = −17 →

Answer key

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

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