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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 504 · 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. 1.5x + 3y = 20 and 4x − 6y = −26 →
  2. 2.2x + 6y = −10 and 6x + 2y = 2 →
  3. 3.x + 9y = 20 and 9x + y = −60 →
  4. 4.5x + 6y = −3 and 6x + 3y = −12 →
  5. 5.3x + 3y = 24 and 4x + 2y = 34 →
  6. 6.3x − 5y = 33 and 2x + 2y = −26 →
  7. 7.2x + y = −18 and x + 2y = −15 →
  8. 8.5x − 2y = 29 and 5x + 3y = 19 →
  9. 9.3x + 6y = −21 and 2x + y = 7 →
  10. 10.2x + 5y = 1 and 5x + 4y = −23 →
  11. 11.7x + 4y = 22 and 4x + 7y = −11 →
  12. 12.6x + 6y = 66 and 6x + y = 21 →
  13. 13.2x + 7y = −6 and 7x + 2y = 24 →
  14. 14.x − 6y = −31 and 4x + 2y = 32 →
  15. 15.3x − y = 20 and x + 5y = 28 →
  16. 16.4x + 2y = 16 and x − 6y = 17 →
  17. 17.x − 6y = −38 and 4x + y = −27 →
  18. 18.5x + 2y = −5 and 2x + 5y = 19 →
  19. 19.4x − y = 20 and 6x + 2y = 44 →
  20. 20.x + 4y = 29 and x − 5y = −25 →
  21. 21.6x + 4y = 2 and 5x + y = 4 →
  22. 22.5x + y = −43 and x + 5y = −47 →
  23. 23.2x + 5y = −19 and 3x + 4y = −18 →
  24. 24.4x − y = −18 and x − 5y = −14 →
  25. 25.x − 5y = −18 and x + 6y = 37 →
  26. 26.2x + y = 16 and 6x + 5y = 44 →
  27. 27.x + 3y = 10 and 3x + y = −2 →
  28. 28.3x + 5y = 20 and 5x − 6y = 19 →
  29. 29.5x + y = 7 and 6x + 3y = 12 →
  30. 30.x + 3y = 5 and 5x + 2y = 12 →
  31. 31.4x + 9y = −43 and 9x + 4y = 17 →
  32. 32.3x − 2y = 15 and x + 2y = 13 →
  33. 33.6x + 5y = 33 and 2x − y = 3 →
  34. 34.4x + 4y = −8 and x + 6y = 3 →
  35. 35.3x + 2y = 10 and 4x + 3y = 14 →
  36. 36.3x + 5y = 18 and 5x + 3y = 14 →
  37. 37.2x + 6y = 38 and 6x + 2y = −30 →
  38. 38.2x + 5y = −12 and 5x − 5y = 40 →
  39. 39.6x + 3y = −48 and 5x + y = −43 →
  40. 40.5x − 3y = 4 and 2x + 6y = 16 →

Answer key

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

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