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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 973 · 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. 1.9x + y = −75 and x + 9y = 45 →
  2. 2.3x − 2y = 20 and x − 2y = 12 →
  3. 3.3x + 2y = 28 and 2x + 3y = 32 →
  4. 4.4x + 7y = −27 and 7x + 4y = 27 →
  5. 5.6x + 5y = −16 and 2x − 3y = −24 →
  6. 6.8x + 4y = −36 and 4x + 8y = 24 →
  7. 7.x + 6y = 57 and 6x + 2y = 36 →
  8. 8.6x + 9y = −6 and 9x + 6y = 6 →
  9. 9.x − 2y = 13 and 6x + 2y = −6 →
  10. 10.x + 2y = −2 and 4x + 4y = 4 →
  11. 11.2x + 3y = 19 and 3x + 2y = 26 →
  12. 12.7x + 2y = 30 and 2x + 7y = 15 →
  13. 13.x + 6y = −8 and 6x + y = 22 →
  14. 14.5x + y = 8 and 2x + y = 5 →
  15. 15.5x + 9y = −46 and 9x + 5y = −38 →
  16. 16.3x − 6y = 39 and 5x + 5y = −25 →
  17. 17.x + y = 12 and 6x + y = 52 →
  18. 18.4x + 6y = 32 and x + y = 6 →
  19. 19.2x + 3y = 8 and 4x + 5y = 18 →
  20. 20.3x + 6y = 72 and 6x + 3y = 72 →
  21. 21.x + 2y = −16 and 3x − 4y = 42 →
  22. 22.4x − 5y = −15 and 4x + 3y = −23 →
  23. 23.2x + 4y = 18 and 3x + 5y = 26 →
  24. 24.2x + y = 16 and 2x − 6y = −26 →
  25. 25.x − 5y = 27 and x + 4y = −9 →
  26. 26.6x + 8y = 70 and 8x + 6y = 84 →
  27. 27.x − 6y = −10 and 4x + 5y = 18 →
  28. 28.2x + 2y = 6 and 3x + 6y = −9 →
  29. 29.5x + 6y = 51 and 4x + y = 37 →
  30. 30.3x + 4y = 23 and 2x + 2y = 16 →
  31. 31.8x + 3y = 54 and 3x + 8y = 34 →
  32. 32.5x − y = −13 and x + 6y = 16 →
  33. 33.4x − 6y = 8 and 3x − 5y = 5 →
  34. 34.9x + 4y = 29 and 4x + 9y = 49 →
  35. 35.2x + 4y = −42 and 2x + 2y = −30 →
  36. 36.5x − 5y = −15 and 6x − 4y = −6 →
  37. 37.5x + y = 38 and 5x + 3y = 54 →
  38. 38.x − y = 5 and 6x + 2y = 6 →
  39. 39.4x + y = −41 and x + 4y = −44 →
  40. 40.2x − 2y = 32 and x + 3y = −12 →

Answer key

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

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