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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 312 · 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 − 6y = −11 and 3x + 6y = 51 →
  2. 2.6x + 3y = 21 and 5x − 5y = 10 →
  3. 3.4x + y = 15 and 2x + 6y = 24 →
  4. 4.x + 5y = −3 and 6x + y = 40 →
  5. 5.5x + 2y = 22 and 6x + 6y = 30 →
  6. 6.4x + 3y = −31 and 3x + 4y = −32 →
  7. 7.3x + 6y = 3 and 2x − 4y = −22 →
  8. 8.x − 6y = −42 and 2x + 4y = 44 →
  9. 9.6x + 7y = −10 and 7x + 6y = −3 →
  10. 10.3x + 6y = −45 and x − 5y = 34 →
  11. 11.x + 9y = −38 and 9x + y = −22 →
  12. 12.4x + 6y = 24 and 6x + 4y = 46 →
  13. 13.3x − 2y = −21 and 3x + 2y = 15 →
  14. 14.5x + 6y = −43 and 6x + 5y = −45 →
  15. 15.7x + 2y = −3 and 2x + 7y = 57 →
  16. 16.2x + 4y = 30 and 3x − 6y = −27 →
  17. 17.9x + 5y = 92 and 5x + 9y = 76 →
  18. 18.2x + 7y = −2 and 7x + 2y = 38 →
  19. 19.2x + 5y = 12 and x + 5y = 16 →
  20. 20.5x + y = −17 and 3x + y = −7 →
  21. 21.x − 6y = −24 and 3x + y = 23 →
  22. 22.5x − 2y = 38 and 6x − 2y = 46 →
  23. 23.6x − y = 16 and 4x + y = 4 →
  24. 24.x − 2y = −5 and 5x + 4y = 59 →
  25. 25.5x + 8y = −41 and 8x + 5y = −50 →
  26. 26.2x − 3y = 37 and 6x − 2y = 62 →
  27. 27.x + 5y = −9 and 2x − y = 15 →
  28. 28.5x + y = 9 and 6x − 2y = 30 →
  29. 29.4x + y = −10 and x + 4y = −10 →
  30. 30.x + 3y = −17 and 2x − 2y = 30 →
  31. 31.7x + 3y = 78 and 3x + 7y = 62 →
  32. 32.4x + y = 29 and 4x − 5y = −1 →
  33. 33.9x + 5y = 77 and 5x + 9y = 49 →
  34. 34.6x + 3y = 30 and x − 2y = 25 →
  35. 35.2x + 5y = 47 and 5x + 2y = 23 →
  36. 36.2x + 7y = −12 and 7x + 2y = 48 →
  37. 37.5x + 2y = 10 and 2x + 5y = −17 →
  38. 38.5x + 6y = 64 and 2x + 3y = 28 →
  39. 39.4x + 3y = 1 and 3x + 4y = −15 →
  40. 40.7x + 5y = 32 and 5x + 7y = 40 →

Answer key

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

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