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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 387 · 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. 1.6x + 5y = −70 and x + 5y = −45 →
  2. 2.2x + y = 2 and x + 2y = −2 →
  3. 3.2x + 4y = 34 and 4x + 2y = 32 →
  4. 4.x + 3y = −13 and 2x − 3y = 28 →
  5. 5.5x − 2y = 27 and 3x − y = 18 →
  6. 6.8x + 6y = 36 and 6x + 8y = 34 →
  7. 7.7x + 2y = 65 and 2x + 7y = 70 →
  8. 8.3x + 6y = −66 and 6x + 3y = −60 →
  9. 9.2x + 3y = 23 and 6x + 2y = 34 →
  10. 10.4x + 9y = 42 and 9x + 4y = 62 →
  11. 11.4x + 2y = 30 and 2x + 4y = 36 →
  12. 12.4x − 3y = −4 and 5x + 4y = 57 →
  13. 13.4x + 2y = −6 and x + 4y = 16 →
  14. 14.x − y = 3 and 5x − 3y = 7 →
  15. 15.4x + 5y = −22 and 5x + y = 4 →
  16. 16.5x + 5y = 10 and x + 4y = −10 →
  17. 17.4x + 3y = 11 and 3x + 4y = 3 →
  18. 18.5x + 5y = −15 and 3x − 2y = 36 →
  19. 19.9x + 3y = 18 and 3x + 9y = −42 →
  20. 20.4x − 5y = −10 and 5x + 5y = −35 →
  21. 21.7x + 6y = −50 and 6x + 7y = −41 →
  22. 22.4x + y = 10 and x + 4y = 10 →
  23. 23.x + 2y = 18 and 4x − 2y = 2 →
  24. 24.2x − y = 11 and 5x − 4y = 23 →
  25. 25.8x + 6y = −58 and 6x + 8y = −54 →
  26. 26.4x + y = −22 and 2x + 5y = −2 →
  27. 27.4x − 4y = −20 and 2x − 3y = −11 →
  28. 28.x − 5y = 0 and 2x − 5y = −5 →
  29. 29.4x + 3y = 21 and 3x + y = 22 →
  30. 30.4x + 5y = −1 and 4x + 6y = −2 →
  31. 31.5x + 5y = 0 and 5x + 6y = −5 →
  32. 32.5x − 2y = 33 and 5x + y = 36 →
  33. 33.5x + 3y = 38 and 3x + 5y = 26 →
  34. 34.3x + 8y = 51 and 8x + 3y = 26 →
  35. 35.x − y = 1 and 4x + 2y = 46 →
  36. 36.4x + 6y = 6 and 4x − 3y = −21 →
  37. 37.x + 4y = −10 and 4x + y = 5 →
  38. 38.6x + 4y = 66 and 2x + 4y = 38 →
  39. 39.6x + 3y = 69 and 5x − 5y = 5 →
  40. 40.3x + 5y = −12 and 3x + 4y = −9 →

Answer key

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

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