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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 793 · 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 = 31 and 6x + 5y = 24 →
  2. 2.4x − 3y = 0 and 6x + 4y = 34 →
  3. 3.x + 7y = −30 and 7x + y = 30 →
  4. 4.4x + 7y = 56 and 7x + 4y = 65 →
  5. 5.4x + 3y = −50 and x + 6y = −44 →
  6. 6.6x − 3y = −21 and 5x + 6y = −43 →
  7. 7.3x + 2y = −34 and 2x + 2y = −26 →
  8. 8.x + 5y = −5 and 6x − 3y = 36 →
  9. 9.2x + 6y = −24 and 6x + 2y = −40 →
  10. 10.2x + 5y = −31 and 2x − y = 11 →
  11. 11.5x − 2y = −21 and 6x + 3y = −36 →
  12. 12.3x + 4y = −6 and 2x − 4y = 16 →
  13. 13.2x + 3y = 22 and 5x + 2y = 11 →
  14. 14.4x + 3y = 26 and 3x + 6y = 42 →
  15. 15.x − 2y = −6 and 3x + 6y = 6 →
  16. 16.5x + 4y = 33 and 6x + 2y = 20 →
  17. 17.4x + 2y = 0 and 4x + 5y = −12 →
  18. 18.9x + 3y = 3 and 3x + 9y = 57 →
  19. 19.3x + y = −5 and 2x + 2y = 2 →
  20. 20.2x + 6y = 38 and 6x + 2y = 50 →
  21. 21.x + 5y = 33 and 2x − 6y = −30 →
  22. 22.2x − 6y = −28 and 4x + y = 9 →
  23. 23.2x + y = 21 and x + 2y = 18 →
  24. 24.6x + 3y = 39 and 4x + 5y = 47 →
  25. 25.x + 4y = 24 and 4x + y = 21 →
  26. 26.3x − 5y = 54 and 4x + 5y = −33 →
  27. 27.x + 2y = −10 and 3x + 3y = −24 →
  28. 28.9x + 5y = 44 and 5x + 9y = 68 →
  29. 29.5x + 4y = −13 and 3x + 4y = −11 →
  30. 30.3x − y = −1 and 6x − 6y = −18 →
  31. 31.8x + 3y = 49 and 3x + 8y = 39 →
  32. 32.7x + 8y = −57 and 8x + 7y = −48 →
  33. 33.5x + 5y = 0 and 2x + y = −1 →
  34. 34.3x + 5y = 47 and 5x + 3y = 41 →
  35. 35.x − 2y = 18 and 3x − 5y = 46 →
  36. 36.3x + 2y = 2 and 4x − 6y = 72 →
  37. 37.8x + 4y = 68 and 4x + 8y = 52 →
  38. 38.x − y = 4 and 6x + y = 52 →
  39. 39.5x + 9y = 33 and 9x + 5y = −19 →
  40. 40.x + 2y = −1 and 2x + y = 1 →

Answer key

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

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