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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 682 · 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. 1.5x + 2y = −35 and 2x + 6y = 12 →
  2. 2.3x + 2y = 15 and 2x + 3y = 20 →
  3. 3.2x + y = −3 and x + 2y = −3 →
  4. 4.2x + y = 24 and x − 2y = −3 →
  5. 5.3x − 2y = 10 and 3x + 5y = 17 →
  6. 6.5x + y = 40 and x + 5y = 32 →
  7. 7.2x + 6y = 40 and 6x + 2y = 8 →
  8. 8.2x − 5y = 49 and x + 2y = −16 →
  9. 9.x + 6y = 20 and x − y = −1 →
  10. 10.3x + 6y = 54 and 6x − 6y = −36 →
  11. 11.x + 2y = 19 and x + y = 13 →
  12. 12.2x + y = 2 and 4x − 4y = −44 →
  13. 13.4x − 2y = −8 and 3x − 5y = −27 →
  14. 14.3x + y = 20 and 5x + 2y = 35 →
  15. 15.8x + y = 49 and x + 8y = 14 →
  16. 16.7x + 3y = −41 and 3x + 7y = −69 →
  17. 17.2x − 3y = 22 and 2x + y = −2 →
  18. 18.2x + y = 15 and 4x + 5y = 51 →
  19. 19.2x − 3y = −38 and 2x + 3y = 10 →
  20. 20.6x + y = 57 and 2x + y = 21 →
  21. 21.3x + 8y = 16 and 8x + 3y = −49 →
  22. 22.4x + 5y = −42 and 3x + 2y = −21 →
  23. 23.2x + 4y = 14 and 2x + 2y = 2 →
  24. 24.4x + 3y = 10 and 4x − 6y = 28 →
  25. 25.4x + 2y = 0 and 3x + y = 1 →
  26. 26.4x − 3y = 17 and 4x − 5y = 15 →
  27. 27.2x + 6y = 64 and 6x + 5y = 88 →
  28. 28.x − 2y = −3 and 2x − 5y = −10 →
  29. 29.4x + 2y = 0 and 2x − 5y = −12 →
  30. 30.x − 3y = −9 and 6x − 4y = 16 →
  31. 31.2x + 8y = 6 and 8x + 2y = −66 →
  32. 32.2x + y = 3 and 2x − 3y = −1 →
  33. 33.3x + 3y = 3 and 3x + 5y = 11 →
  34. 34.4x + y = 43 and x + 5y = 44 →
  35. 35.5x + 7y = 28 and 7x + 5y = 44 →
  36. 36.5x + 4y = 52 and 4x + 5y = 47 →
  37. 37.5x − y = −1 and 3x − y = −3 →
  38. 38.2x − 5y = −27 and 3x + 4y = 63 →
  39. 39.6x + 2y = −22 and 2x + 6y = −18 →
  40. 40.4x + 2y = 40 and x + 5y = 46 →

Answer key

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

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