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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 289 · 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. 1.9x + 8y = −121 and 8x + 9y = −117 →
  2. 2.x + 8y = 79 and 8x + y = 65 →
  3. 3.4x + 4y = −8 and 3x + 2y = 3 →
  4. 4.x + 5y = 17 and 5x + y = 13 →
  5. 5.x + 3y = 17 and 3x − 4y = −1 →
  6. 6.9x + y = 61 and x + 9y = 69 →
  7. 7.5x − 4y = −51 and 4x − 5y = −57 →
  8. 8.6x + 5y = −10 and 5x + 6y = −1 →
  9. 9.x + y = −1 and 2x + 5y = −8 →
  10. 10.3x + 2y = 23 and 2x + 3y = 22 →
  11. 11.6x + 4y = 44 and 4x + 4y = 32 →
  12. 12.5x − 6y = −49 and x − 6y = −53 →
  13. 13.6x + 4y = −18 and x + 4y = 17 →
  14. 14.6x + 2y = 12 and 3x + 4y = 15 →
  15. 15.3x + 5y = −10 and 5x + 3y = −22 →
  16. 16.4x + 7y = 14 and 7x + 4y = 41 →
  17. 17.6x + 2y = 58 and 2x + 6y = 30 →
  18. 18.x + 6y = 0 and 6x + y = −35 →
  19. 19.4x + 2y = −6 and 3x − 6y = −57 →
  20. 20.5x + y = −17 and x + 2y = 11 →
  21. 21.3x + y = −22 and x + 6y = −30 →
  22. 22.5x − 3y = 6 and 2x + 5y = 21 →
  23. 23.3x + 5y = 32 and 2x + y = 19 →
  24. 24.2x − 4y = 0 and x − 3y = −3 →
  25. 25.3x + 2y = 22 and 2x + 3y = 18 →
  26. 26.2x − 5y = 13 and 4x − 4y = 20 →
  27. 27.6x + 2y = −22 and 2x + 6y = 30 →
  28. 28.3x + y = 6 and 2x + 6y = 52 →
  29. 29.7x + 9y = 74 and 9x + 7y = 86 →
  30. 30.6x + 5y = 17 and 4x − 5y = −47 →
  31. 31.2x + 7y = −53 and 7x + 2y = −28 →
  32. 32.5x − 2y = −22 and 6x + 5y = −56 →
  33. 33.6x − 2y = −58 and x − 3y = −23 →
  34. 34.2x + y = 7 and x + 2y = 2 →
  35. 35.5x − y = 6 and 5x − 2y = 2 →
  36. 36.3x + y = 25 and x + 3y = 19 →
  37. 37.x + 3y = 14 and x − 5y = −2 →
  38. 38.2x − 2y = −12 and 3x + 2y = −8 →
  39. 39.7x + 3y = −27 and 3x + 7y = 17 →
  40. 40.6x + 3y = −42 and 5x − 5y = −20 →

Answer key

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

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