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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 309 · 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.x − y = −3 and 4x − 6y = −14 →
  2. 2.3x + 4y = 16 and 6x + 2y = 26 →
  3. 3.3x + 6y = 15 and 2x + 5y = 13 →
  4. 4.x + 9y = 10 and 9x + y = 10 →
  5. 5.3x + 2y = 5 and x − 2y = −17 →
  6. 6.4x + 3y = 57 and 3x + 4y = 55 →
  7. 7.5x − y = 10 and 3x + 2y = −7 →
  8. 8.4x + y = −21 and x + 4y = 21 →
  9. 9.5x + 6y = 4 and 4x + 3y = −4 →
  10. 10.6x + 4y = 30 and 2x − y = −11 →
  11. 11.6x + 7y = 10 and 7x + 6y = 3 →
  12. 12.6x − 4y = 82 and 2x + y = 11 →
  13. 13.4x + 3y = 19 and 3x + 4y = 16 →
  14. 14.3x − 6y = 48 and 5x − 3y = 38 →
  15. 15.4x − 2y = 38 and 5x − 6y = 79 →
  16. 16.x + 6y = 63 and x + y = 18 →
  17. 17.2x + 2y = 2 and 4x − y = 44 →
  18. 18.4x + 8y = 96 and 8x + 4y = 96 →
  19. 19.7x + 9y = −3 and 9x + 7y = −13 →
  20. 20.2x + y = 4 and 2x − 5y = −32 →
  21. 21.4x + 2y = 30 and 4x − 3y = 5 →
  22. 22.2x − 3y = −8 and 2x + 2y = 2 →
  23. 23.x + 5y = 0 and 2x − 2y = 12 →
  24. 24.6x + y = 14 and 3x + y = 8 →
  25. 25.8x + 2y = 76 and 2x + 8y = 34 →
  26. 26.5x + y = 16 and 4x + 3y = 26 →
  27. 27.5x + 6y = 47 and 2x + 4y = 30 →
  28. 28.x + 4y = 6 and 4x + y = −21 →
  29. 29.2x + 4y = −18 and 6x + y = 12 →
  30. 30.2x − 4y = −10 and 3x − y = 15 →
  31. 31.x + 4y = −40 and 3x + y = −21 →
  32. 32.3x − 3y = −39 and 3x + 3y = 15 →
  33. 33.8x + y = 23 and x + 8y = −68 →
  34. 34.x + 8y = −34 and 8x + y = −20 →
  35. 35.5x + 9y = 101 and 9x + 5y = 81 →
  36. 36.2x + y = −14 and 2x − 5y = −26 →
  37. 37.5x + 9y = 68 and 9x + 5y = 44 →
  38. 38.2x + 6y = 8 and 2x + 5y = 7 →
  39. 39.6x − y = −34 and x + 6y = 19 →
  40. 40.5x − y = −4 and x + y = 10 →

Answer key

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

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