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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 587 · 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 = −7 and 6x + 5y = 7 →
  2. 2.x − y = 5 and x + 3y = 9 →
  3. 3.2x + y = −19 and x + 2y = −20 →
  4. 4.2x + y = −2 and 6x − 5y = −38 →
  5. 5.5x − y = 12 and 4x + 6y = −38 →
  6. 6.5x + y = 45 and 4x − 4y = 12 →
  7. 7.4x + y = −7 and 2x + 2y = 4 →
  8. 8.5x + 8y = 2 and 8x + 5y = 11 →
  9. 9.6x − y = 24 and 4x + y = 26 →
  10. 10.2x − 3y = −23 and 5x + 6y = 64 →
  11. 11.6x + y = 33 and 2x − 2y = −10 →
  12. 12.4x + 6y = 80 and 6x − 5y = 8 →
  13. 13.6x + 5y = 29 and 4x − 6y = 66 →
  14. 14.x + 5y = −20 and 6x + 3y = −39 →
  15. 15.4x − 2y = 20 and 3x − 5y = −13 →
  16. 16.5x + 3y = 38 and 4x − 2y = 26 →
  17. 17.3x + 2y = 5 and 2x + 3y = 0 →
  18. 18.2x + 6y = 2 and 6x − 4y = −16 →
  19. 19.5x − 6y = −16 and 3x + 3y = −3 →
  20. 20.5x + 2y = 20 and 4x + 5y = 33 →
  21. 21.7x + 6y = 77 and 6x + 7y = 79 →
  22. 22.x + 9y = 80 and 9x + y = 0 →
  23. 23.4x + 4y = 4 and x + 2y = 9 →
  24. 24.5x + y = −52 and 4x + 2y = −50 →
  25. 25.x + 5y = 2 and 2x + 5y = −1 →
  26. 26.5x − 3y = 44 and 3x + 4y = −20 →
  27. 27.5x + 2y = 3 and 2x + 5y = 39 →
  28. 28.5x + 9y = 3 and 9x + 5y = −17 →
  29. 29.2x + 6y = −20 and 6x + 2y = −28 →
  30. 30.x + 6y = 45 and x − 6y = −27 →
  31. 31.2x + 3y = 0 and 6x + 3y = 12 →
  32. 32.8x + y = −34 and x + 8y = −20 →
  33. 33.3x + 2y = −6 and 2x + 3y = 1 →
  34. 34.3x + 3y = −18 and 3x + 6y = −15 →
  35. 35.4x − 5y = −15 and x − 6y = −37 →
  36. 36.x − 6y = −28 and 3x + 5y = 31 →
  37. 37.3x + 2y = 27 and 6x + y = 45 →
  38. 38.x + 8y = 29 and 8x + y = 43 →
  39. 39.2x − 5y = 7 and 2x + 4y = 16 →
  40. 40.2x − 3y = 17 and 5x − 5y = 35 →

Answer key

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

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