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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 110 · 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 − y = 25 and 2x + y = 5 →
  2. 2.x + y = 1 and x − 2y = 7 →
  3. 3.2x − 2y = 12 and 6x + 5y = −8 →
  4. 4.4x − 5y = −7 and 3x + 6y = 24 →
  5. 5.5x − 5y = 80 and 5x − 4y = 73 →
  6. 6.2x + 2y = 20 and x + 6y = 50 →
  7. 7.3x + y = 6 and 5x + y = 8 →
  8. 8.5x + 3y = −33 and 4x + y = −18 →
  9. 9.3x − y = −30 and 2x − 4y = −50 →
  10. 10.6x + 3y = 54 and 3x + 6y = 63 →
  11. 11.2x + 6y = −14 and 2x + y = 1 →
  12. 12.8x + y = 27 and x + 8y = −36 →
  13. 13.2x + 8y = −54 and 8x + 2y = −6 →
  14. 14.4x + 5y = 9 and 4x − 5y = −1 →
  15. 15.4x − 4y = −32 and 2x + 6y = 40 →
  16. 16.5x + 2y = 15 and 5x + 3y = 20 →
  17. 17.4x + 6y = 44 and 3x + 4y = 30 →
  18. 18.3x − 4y = 17 and 6x − 2y = 22 →
  19. 19.x + 3y = 32 and 5x − 4y = −11 →
  20. 20.3x + 4y = 19 and 2x − 2y = 8 →
  21. 21.x + 4y = 25 and x + 6y = 37 →
  22. 22.4x + y = 2 and x + 4y = −22 →
  23. 23.3x + 4y = −4 and 5x − 6y = −70 →
  24. 24.x + 9y = 44 and 9x + y = −4 →
  25. 25.5x − y = 47 and 4x − 6y = 48 →
  26. 26.2x − 6y = −60 and 2x + 2y = 4 →
  27. 27.7x + 3y = 70 and 3x + 7y = 70 →
  28. 28.6x + 2y = −36 and 2x + 6y = −44 →
  29. 29.4x + 3y = −16 and 3x + 4y = −5 →
  30. 30.4x + 5y = −41 and 3x − 6y = 57 →
  31. 31.2x − 3y = −16 and x + 4y = 25 →
  32. 32.x + 4y = −5 and 4x − 2y = 16 →
  33. 33.6x + y = 13 and 2x + 3y = 23 →
  34. 34.5x + 6y = −4 and 6x + 5y = −7 →
  35. 35.6x + 2y = −50 and 3x + 4y = −19 →
  36. 36.2x + y = −7 and 5x + 2y = −15 →
  37. 37.6x − y = 15 and 5x − y = 12 →
  38. 38.6x + 8y = −80 and 8x + 6y = −88 →
  39. 39.6x + 2y = 2 and 5x + 3y = −5 →
  40. 40.x − 5y = −31 and 6x − 6y = −66 →

Answer key

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

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