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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 553 · 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 + 9y = 50 and 9x + y = 50 →
  2. 2.5x + y = 43 and x + 5y = 23 →
  3. 3.x + 3y = 6 and 3x + y = −6 →
  4. 4.x + 7y = 28 and 7x + y = 52 →
  5. 5.4x + 2y = 18 and x + 3y = 22 →
  6. 6.4x + 5y = 62 and 5x − y = 34 →
  7. 7.2x + 2y = 4 and x + 3y = 12 →
  8. 8.4x + y = −3 and x + 4y = 18 →
  9. 9.x + 4y = 25 and 4x + y = −5 →
  10. 10.2x + 8y = 90 and 8x + 2y = 90 →
  11. 11.3x + 7y = 55 and 7x + 3y = 75 →
  12. 12.3x + 9y = 51 and 9x + 3y = −15 →
  13. 13.4x − 4y = −4 and 5x + 4y = 76 →
  14. 14.3x + 6y = 33 and x − 2y = −9 →
  15. 15.6x − 4y = 0 and x + 2y = 8 →
  16. 16.6x + 5y = 75 and x + y = 14 →
  17. 17.8x + 6y = 58 and 6x + 8y = 54 →
  18. 18.3x + 2y = 12 and 2x + 3y = 13 →
  19. 19.4x + 7y = 72 and 7x + 4y = 60 →
  20. 20.x + 2y = 8 and 5x − y = 18 →
  21. 21.5x + 3y = 39 and 3x + 3y = 33 →
  22. 22.5x + y = 21 and 4x + 4y = 4 →
  23. 23.3x + 4y = −31 and 3x − 6y = −21 →
  24. 24.3x − 4y = 26 and 5x + 4y = 22 →
  25. 25.5x + 6y = −22 and 3x − 2y = −30 →
  26. 26.x + y = 5 and 2x + 3y = 12 →
  27. 27.5x − 6y = −26 and 3x + y = −11 →
  28. 28.x + 3y = 5 and 6x − 5y = 7 →
  29. 29.4x + 9y = 99 and 9x + 4y = 109 →
  30. 30.8x + 9y = −38 and 9x + 8y = −47 →
  31. 31.4x − 2y = −14 and x + 3y = 14 →
  32. 32.3x + 4y = −21 and 4x + 3y = −21 →
  33. 33.3x + 6y = 39 and 2x − 2y = −4 →
  34. 34.5x + 3y = −19 and x − y = −7 →
  35. 35.3x + 6y = −45 and x + 3y = −23 →
  36. 36.5x + 2y = −13 and 4x + 4y = −32 →
  37. 37.9x + 3y = 24 and 3x + 9y = 0 →
  38. 38.5x + 8y = 89 and 8x + 5y = 80 →
  39. 39.4x − 6y = 38 and 6x + 5y = −13 →
  40. 40.7x + y = −42 and x + 7y = 42 →

Answer key

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

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