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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 353 · 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 + 5y = −30 and 5x − y = 0 →
  2. 2.6x + 5y = 34 and x + 3y = 10 →
  3. 3.2x − 4y = −4 and 6x + 6y = 24 →
  4. 4.2x + 4y = 38 and 5x − 4y = −17 →
  5. 5.3x + 5y = 23 and x + 5y = 21 →
  6. 6.8x + 7y = 113 and 7x + 8y = 112 →
  7. 7.2x + 2y = 12 and 3x − 6y = −45 →
  8. 8.2x + y = −17 and 3x − 5y = −19 →
  9. 9.4x + 2y = 20 and 2x + 4y = 28 →
  10. 10.2x + 9y = 35 and 9x + 2y = 42 →
  11. 11.7x + 6y = 50 and 6x + 7y = 54 →
  12. 12.3x + 5y = 21 and 5x + 3y = −13 →
  13. 13.2x + 3y = 10 and x + 3y = 11 →
  14. 14.3x + y = −12 and 2x − 2y = −24 →
  15. 15.x − y = 7 and 4x + 4y = 36 →
  16. 16.2x + 6y = 36 and 5x + 3y = 6 →
  17. 17.4x + 3y = −10 and 3x − 6y = 9 →
  18. 18.5x + 2y = 48 and 5x + 3y = 57 →
  19. 19.4x + 5y = 61 and 5x + 4y = 56 →
  20. 20.5x + 3y = 61 and 3x + 5y = 59 →
  21. 21.6x + y = 27 and 6x + 5y = 63 →
  22. 22.3x + 5y = 12 and 5x + 5y = 0 →
  23. 23.x − 4y = 21 and 3x − 2y = 3 →
  24. 24.8x + 3y = −51 and 3x + 8y = 29 →
  25. 25.x + 9y = 10 and 9x + y = −70 →
  26. 26.2x + 8y = 2 and 8x + 2y = 38 →
  27. 27.6x + 3y = 45 and 3x + y = 23 →
  28. 28.4x + 5y = −39 and 6x − y = 1 →
  29. 29.x − 4y = −24 and 2x + 6y = 8 →
  30. 30.3x + 5y = 23 and 5x + y = 31 →
  31. 31.3x + 8y = 14 and 8x + 3y = 19 →
  32. 32.x − y = −4 and 4x − y = 8 →
  33. 33.6x + 5y = −7 and 2x − 2y = 16 →
  34. 34.5x + 7y = 8 and 7x + 5y = 16 →
  35. 35.5x + 4y = 25 and 2x + 5y = 27 →
  36. 36.5x + 3y = 32 and x + 5y = 46 →
  37. 37.5x + 3y = −54 and 3x + 5y = −58 →
  38. 38.2x + 4y = 12 and 4x + 2y = 18 →
  39. 39.3x − 6y = −27 and 5x − 6y = −13 →
  40. 40.9x + 4y = −28 and 4x + 9y = 2 →

Answer key

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

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