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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 487 · 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.x + 2y = 11 and x + 4y = 21 →
  2. 2.9x + y = −63 and x + 9y = 73 →
  3. 3.6x + 8y = −70 and 8x + 6y = −70 →
  4. 4.6x + 5y = 43 and 3x + 5y = 34 →
  5. 5.2x − 2y = 0 and 3x + 3y = 12 →
  6. 6.3x − 4y = 0 and 4x + 5y = 62 →
  7. 7.6x + 3y = 57 and 3x − y = 26 →
  8. 8.6x + 2y = −24 and 4x + 3y = −1 →
  9. 9.4x + 6y = −20 and x − 6y = 55 →
  10. 10.3x − 4y = 5 and 5x + 5y = 20 →
  11. 11.5x + 2y = 29 and 2x − 2y = 6 →
  12. 12.6x − y = 21 and 6x − 2y = 30 →
  13. 13.x + 3y = 11 and 4x + 5y = 23 →
  14. 14.5x + 4y = 31 and 4x + 2y = 14 →
  15. 15.x − 2y = −7 and x + 4y = 17 →
  16. 16.7x + 9y = −85 and 9x + 7y = −91 →
  17. 17.2x + 3y = 0 and 5x − 5y = −75 →
  18. 18.6x + 8y = −6 and 8x + 6y = 6 →
  19. 19.5x + 5y = −35 and x + 6y = −22 →
  20. 20.5x + 4y = −53 and 6x + 6y = −66 →
  21. 21.3x + y = −17 and x + 3y = −27 →
  22. 22.6x − 3y = 33 and 4x + 4y = −20 →
  23. 23.7x + 8y = −11 and 8x + 7y = −19 →
  24. 24.6x + 3y = 27 and 5x − 6y = −37 →
  25. 25.5x − 3y = 27 and x − 2y = −3 →
  26. 26.2x + 6y = 28 and 3x + 2y = 21 →
  27. 27.3x + 4y = 44 and 4x + 3y = 47 →
  28. 28.2x + y = 7 and x + 2y = −1 →
  29. 29.4x + 2y = −18 and 2x + 4y = −6 →
  30. 30.4x − y = 31 and 5x − y = 40 →
  31. 31.2x + 3y = 13 and 3x + 4y = 17 →
  32. 32.5x + 4y = 47 and x − 4y = −5 →
  33. 33.x + 3y = 32 and 6x − 2y = 12 →
  34. 34.x + 5y = 36 and 5x + y = 36 →
  35. 35.x + 3y = 20 and 6x + 4y = 8 →
  36. 36.3x − 5y = 38 and 5x + 2y = −9 →
  37. 37.6x − 2y = 44 and 5x − 5y = 30 →
  38. 38.6x + 6y = −96 and 2x + 4y = −48 →
  39. 39.8x + 9y = −77 and 9x + 8y = −76 →
  40. 40.4x − 4y = 8 and 4x + 2y = −10 →

Answer key

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

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