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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 196 · 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. 1.4x + 9y = −37 and 9x + 4y = −2 →
  2. 2.6x + 5y = 55 and 6x − 5y = 5 →
  3. 3.5x − 4y = 52 and x − y = 12 →
  4. 4.3x − 4y = 16 and 4x + 2y = −30 →
  5. 5.2x + y = 23 and 6x + 6y = 96 →
  6. 6.3x − 4y = 5 and 2x + 2y = 8 →
  7. 7.6x + y = −3 and x + 6y = 17 →
  8. 8.6x + y = −51 and 2x + 6y = 0 →
  9. 9.9x + 8y = −16 and 8x + 9y = −1 →
  10. 10.3x + 4y = 42 and x + 4y = 38 →
  11. 11.6x + 6y = 54 and 5x + y = 17 →
  12. 12.8x + 5y = −52 and 5x + 8y = −13 →
  13. 13.2x + 3y = 2 and 2x + y = −2 →
  14. 14.3x + 5y = 8 and x + 4y = 5 →
  15. 15.5x + 2y = 24 and x + 6y = 16 →
  16. 16.x − 2y = −5 and 5x + 2y = −49 →
  17. 17.x + 5y = 33 and 5x + y = −3 →
  18. 18.3x + 4y = 16 and 5x − 4y = −48 →
  19. 19.6x + y = 41 and 2x + 4y = 10 →
  20. 20.3x + y = 15 and x + 3y = −19 →
  21. 21.4x + y = 29 and x + 4y = 11 →
  22. 22.5x + 8y = 112 and 8x + 5y = 109 →
  23. 23.3x + 2y = 17 and 2x + 3y = 13 →
  24. 24.5x + y = 21 and 2x + y = 9 →
  25. 25.2x + 6y = 18 and 5x + 6y = 36 →
  26. 26.2x − 2y = 6 and x + 4y = −22 →
  27. 27.5x + y = 46 and 4x − 2y = 34 →
  28. 28.5x − 6y = −20 and 5x + 5y = 35 →
  29. 29.7x + 4y = −41 and 4x + 7y = −14 →
  30. 30.3x + 5y = −37 and 6x + 4y = −26 →
  31. 31.x − 3y = −25 and 5x + 4y = 46 →
  32. 32.6x + 8y = 38 and 8x + 6y = 32 →
  33. 33.2x − 4y = 22 and 6x + 2y = −46 →
  34. 34.3x + 4y = 18 and 4x + 3y = 10 →
  35. 35.x − y = 5 and 3x + y = 7 →
  36. 36.4x + 6y = 26 and 6x + 4y = 24 →
  37. 37.6x + 5y = −3 and 5x + 6y = 14 →
  38. 38.5x + y = −37 and x + 5y = −41 →
  39. 39.9x + 2y = −11 and 2x + 9y = 66 →
  40. 40.3x + 3y = 3 and 6x + y = −4 →

Answer key

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

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