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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 337 · 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. 1.3x + 2y = 23 and 2x − 3y = 24 →
  2. 2.x + 9y = −57 and 9x + y = −33 →
  3. 3.6x − 4y = 18 and 4x − y = −3 →
  4. 4.6x − 2y = 40 and 2x − 6y = 8 →
  5. 5.5x − y = 32 and 4x − 6y = 36 →
  6. 6.2x + 2y = 20 and 3x + y = 22 →
  7. 7.3x − 6y = −75 and x + 2y = 11 →
  8. 8.4x + 7y = −38 and 7x + 4y = −17 →
  9. 9.x − 6y = 20 and 5x + 5y = 30 →
  10. 10.6x + 5y = −8 and x − 4y = −11 →
  11. 11.4x + 8y = 12 and 8x + 4y = 0 →
  12. 12.7x + 3y = −29 and 3x + 7y = −41 →
  13. 13.5x + 2y = 11 and 2x + 5y = −4 →
  14. 14.4x − y = 10 and 5x + 2y = 19 →
  15. 15.x − y = −1 and x + y = 11 →
  16. 16.3x + 4y = 10 and 6x + y = −29 →
  17. 17.x − 6y = −34 and 4x + 2y = −6 →
  18. 18.6x − 5y = 23 and 2x + y = −11 →
  19. 19.5x + 6y = −13 and 2x + 2y = −4 →
  20. 20.x + 4y = 10 and 4x + y = −5 →
  21. 21.x + 3y = 25 and 3x + y = 3 →
  22. 22.6x + 5y = −34 and 6x + y = −26 →
  23. 23.3x + 5y = 0 and 5x + 3y = −16 →
  24. 24.3x + 6y = −30 and 6x + 3y = 21 →
  25. 25.2x + 5y = 47 and 2x + y = 19 →
  26. 26.5x − y = 16 and 5x + 3y = 52 →
  27. 27.2x + y = 25 and 3x − 5y = −8 →
  28. 28.2x + y = 13 and x + 2y = 17 →
  29. 29.5x + 7y = 81 and 7x + 5y = 75 →
  30. 30.4x + 5y = 51 and 5x − 3y = 36 →
  31. 31.4x − 5y = −9 and 4x + y = 21 →
  32. 32.7x + 5y = −43 and 5x + 7y = −17 →
  33. 33.2x + 4y = 44 and 4x + 2y = 40 →
  34. 34.2x − 3y = −7 and 2x + 2y = 8 →
  35. 35.2x + y = 7 and x + 2y = 8 →
  36. 36.6x + 2y = 28 and 4x + 5y = 48 →
  37. 37.9x + 7y = −31 and 7x + 9y = −49 →
  38. 38.6x + 9y = −21 and 9x + 6y = 6 →
  39. 39.2x − y = −1 and 6x + 2y = −8 →
  40. 40.x + 6y = 50 and x + 4y = 36 →

Answer key

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

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