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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 319 · 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. 1.4x + 9y = −10 and 9x + 4y = −55 →
  2. 2.3x + 8y = 17 and 8x + 3y = 27 →
  3. 3.x + 3y = 5 and 6x + 2y = −34 →
  4. 4.2x + 2y = 32 and 4x − 2y = 22 →
  5. 5.3x + y = 7 and 4x + y = 8 →
  6. 6.7x + 4y = 45 and 4x + 7y = 54 →
  7. 7.2x + 5y = −5 and 5x + 2y = 19 →
  8. 8.x − 3y = −19 and 6x − 6y = −6 →
  9. 9.x + 5y = 9 and 3x + 5y = 7 →
  10. 10.5x + 2y = 7 and x − 3y = 32 →
  11. 11.8x + 4y = 60 and 4x + 8y = 48 →
  12. 12.5x + 2y = −13 and 2x + 5y = −1 →
  13. 13.5x + 5y = −25 and x − 6y = −12 →
  14. 14.2x + 9y = 66 and 9x + 2y = 66 →
  15. 15.9x + 2y = 65 and 2x + 9y = 23 →
  16. 16.2x + 5y = −47 and x + 2y = −20 →
  17. 17.x + 5y = 30 and 6x + y = 35 →
  18. 18.3x + y = 5 and x + 4y = 9 →
  19. 19.x + 6y = 52 and 3x + 2y = 28 →
  20. 20.9x + 3y = 33 and 3x + 9y = 75 →
  21. 21.7x + 4y = 30 and 4x + 7y = 36 →
  22. 22.x + 4y = −3 and 4x + 6y = 18 →
  23. 23.9x + 2y = 77 and 2x + 9y = 77 →
  24. 24.2x + 4y = 6 and 5x − 4y = −13 →
  25. 25.5x + y = 41 and x + 2y = 10 →
  26. 26.4x − 3y = 22 and 6x + 5y = −24 →
  27. 27.5x + y = −33 and x + 3y = −1 →
  28. 28.2x + 6y = −16 and 2x − 3y = 29 →
  29. 29.2x + 7y = 15 and 7x + 2y = 30 →
  30. 30.2x + 7y = 52 and 7x + 2y = 2 →
  31. 31.5x + 7y = 49 and 7x + 5y = 59 →
  32. 32.8x + y = −22 and x + 8y = −50 →
  33. 33.x + 2y = −1 and 4x − 2y = −34 →
  34. 34.x + 6y = −39 and 3x + 6y = −57 →
  35. 35.8x + 5y = 46 and 5x + 8y = 19 →
  36. 36.2x + 3y = 5 and 2x + 2y = 2 →
  37. 37.5x + 9y = −12 and 9x + 5y = 12 →
  38. 38.4x + 5y = 49 and 3x − 4y = −2 →
  39. 39.6x + 4y = −42 and 4x + 6y = −18 →
  40. 40.7x + y = 67 and x + 7y = 37 →

Answer key

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

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