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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 950 · 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 + 6y = 12 and 6x + 7y = 1 →
  2. 2.x + 4y = −24 and 4x + y = 9 →
  3. 3.2x + 6y = 2 and 6x + 2y = −10 →
  4. 4.3x + 2y = 13 and 2x + 3y = 17 →
  5. 5.5x − 6y = 34 and 3x − 5y = 19 →
  6. 6.x + 4y = 35 and 3x + 2y = 35 →
  7. 7.3x + y = −20 and x + 3y = −28 →
  8. 8.5x + y = 19 and x − 2y = −5 →
  9. 9.2x + 5y = −37 and x − 6y = 58 →
  10. 10.x + 8y = 65 and 8x + y = 16 →
  11. 11.6x + 8y = 70 and 8x + 6y = 56 →
  12. 12.3x + y = −17 and 4x − 2y = −26 →
  13. 13.x + 5y = 30 and 5x + y = 30 →
  14. 14.4x + y = −24 and 3x + 4y = −5 →
  15. 15.6x + 8y = 64 and 8x + 6y = 62 →
  16. 16.4x + 3y = 35 and 3x + 4y = 28 →
  17. 17.2x + 6y = −12 and 2x − 4y = 18 →
  18. 18.2x − y = 8 and 6x + y = 48 →
  19. 19.4x + 6y = 24 and 6x + 4y = 6 →
  20. 20.3x + 6y = 42 and x + 4y = 26 →
  21. 21.2x + y = 9 and 5x + 3y = 26 →
  22. 22.5x − 4y = −71 and 2x + y = −5 →
  23. 23.6x + 4y = 0 and 4x + 6y = 30 →
  24. 24.3x + 2y = −10 and 2x + 5y = −3 →
  25. 25.3x + 7y = 15 and 7x + 3y = −5 →
  26. 26.5x + 3y = −6 and x + 2y = −11 →
  27. 27.3x + y = 11 and x + 3y = 9 →
  28. 28.6x + 3y = 54 and 2x + 2y = 24 →
  29. 29.4x − y = −15 and 3x + 3y = −45 →
  30. 30.6x + 7y = 4 and 7x + 6y = −4 →
  31. 31.6x + 3y = 33 and 3x − 4y = −33 →
  32. 32.x + 2y = 14 and 4x − 6y = 14 →
  33. 33.5x + 8y = 56 and 8x + 5y = 74 →
  34. 34.4x + 7y = 53 and 7x + 4y = 68 →
  35. 35.6x + 8y = 96 and 8x + 6y = 86 →
  36. 36.6x − y = −45 and 5x + 3y = −3 →
  37. 37.2x − 4y = −32 and 3x + y = −13 →
  38. 38.2x + 5y = −57 and x + 4y = −42 →
  39. 39.2x + y = −10 and x + 2y = −2 →
  40. 40.4x + 2y = −26 and x − 5y = 21 →

Answer key

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

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