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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 970 · 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. 1.8x + 3y = −45 and 3x + 8y = 45 →
  2. 2.3x + 4y = −36 and 4x + 3y = −34 →
  3. 3.2x + 6y = 28 and 6x + 2y = 4 →
  4. 4.2x − y = −4 and 2x + y = 0 →
  5. 5.5x − 2y = 41 and 4x − 2y = 32 →
  6. 6.6x + y = 35 and 5x + 6y = 55 →
  7. 7.6x + y = −23 and x + 5y = 30 →
  8. 8.5x + 8y = −43 and 8x + 5y = −61 →
  9. 9.x − 3y = 28 and 5x − y = 42 →
  10. 10.6x − 3y = −6 and 5x + 2y = 13 →
  11. 11.x + 5y = −10 and 4x − 2y = 26 →
  12. 12.3x + 8y = −76 and 8x + 3y = −56 →
  13. 13.4x + 8y = −52 and 8x + 4y = 4 →
  14. 14.5x + 6y = 5 and 6x + 5y = 17 →
  15. 15.3x − 2y = 4 and x + 5y = 41 →
  16. 16.x + y = −3 and 5x − 6y = −59 →
  17. 17.2x + 2y = −8 and 2x + 6y = −28 →
  18. 18.3x + y = −2 and 5x + 2y = −1 →
  19. 19.5x + 2y = 3 and 3x + 6y = −27 →
  20. 20.4x + y = −20 and x + 4y = −20 →
  21. 21.9x + y = 22 and x + 9y = 38 →
  22. 22.3x + 2y = 3 and 2x + 3y = −13 →
  23. 23.3x + 7y = 52 and 7x + 3y = 68 →
  24. 24.6x + 6y = 72 and x + 2y = 15 →
  25. 25.4x + y = −7 and 2x + 2y = −2 →
  26. 26.5x + 3y = 51 and 2x − 6y = −30 →
  27. 27.6x − 5y = −53 and x − 2y = −17 →
  28. 28.6x + y = −56 and 5x + 6y = −57 →
  29. 29.3x − 2y = 5 and 6x − 3y = 12 →
  30. 30.2x + 5y = 26 and 4x + 5y = 42 →
  31. 31.3x + 7y = 46 and 7x + 3y = 54 →
  32. 32.x + 2y = 19 and 5x − y = −4 →
  33. 33.2x + 4y = −8 and 6x − 6y = 48 →
  34. 34.3x + 5y = −56 and 4x + 5y = −63 →
  35. 35.2x + 9y = −39 and 9x + 2y = 17 →
  36. 36.3x + 4y = 30 and 6x + y = −3 →
  37. 37.x + y = 6 and 2x − 3y = 2 →
  38. 38.5x − 2y = 33 and 4x + 4y = 32 →
  39. 39.8x + 4y = 100 and 4x + 8y = 92 →
  40. 40.4x + 2y = 2 and 2x + 4y = −8 →

Answer key

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

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