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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 705 · 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 = 89 and 2x + 2y = 32 →
  2. 2.3x − 6y = −51 and 3x − 3y = −24 →
  3. 3.8x + 2y = 80 and 2x + 8y = 50 →
  4. 4.2x + 3y = 24 and 3x + 2y = 31 →
  5. 5.3x + 5y = 54 and 2x − 5y = −39 →
  6. 6.3x + y = −24 and 6x + 5y = −66 →
  7. 7.8x + 3y = −33 and 3x + 8y = −33 →
  8. 8.2x − 3y = 8 and 6x + y = 44 →
  9. 9.7x + 6y = 13 and 6x + 7y = 13 →
  10. 10.4x + 2y = −10 and 6x − 2y = 0 →
  11. 11.6x + y = 53 and x + 6y = 38 →
  12. 12.7x + 8y = 97 and 8x + 7y = 98 →
  13. 13.6x + 5y = 66 and 2x + 2y = 24 →
  14. 14.5x + 7y = 2 and 7x + 5y = 22 →
  15. 15.6x + y = −14 and 5x + 4y = −18 →
  16. 16.2x + 2y = 18 and 2x + 6y = 42 →
  17. 17.5x + 2y = −6 and x − 4y = 34 →
  18. 18.5x − 6y = 12 and 2x − 5y = −3 →
  19. 19.5x − 3y = 29 and 5x − 4y = 27 →
  20. 20.4x − 3y = 6 and 3x − 2y = 5 →
  21. 21.x + 4y = 11 and x + 5y = 13 →
  22. 22.6x − 2y = 18 and 6x − y = 15 →
  23. 23.4x − y = 13 and 2x + 6y = −52 →
  24. 24.6x + y = 21 and 2x + 4y = −4 →
  25. 25.6x − y = 45 and 4x − y = 33 →
  26. 26.3x + 4y = −13 and 4x + 3y = −22 →
  27. 27.8x + 2y = 4 and 2x + 8y = 46 →
  28. 28.3x + 5y = 4 and 6x + y = 44 →
  29. 29.9x + y = 20 and x + 9y = −60 →
  30. 30.4x + y = 10 and x + 2y = 13 →
  31. 31.2x − y = 6 and x − 5y = −6 →
  32. 32.3x + 6y = −42 and 6x + 3y = −12 →
  33. 33.2x + y = 19 and 6x − 5y = −15 →
  34. 34.7x + 4y = 75 and 4x + 7y = 57 →
  35. 35.2x + 6y = −40 and 2x − 6y = 68 →
  36. 36.9x + 3y = 15 and 3x + 9y = −51 →
  37. 37.3x + 7y = −7 and 7x + 3y = −43 →
  38. 38.5x − 3y = 12 and 3x − 3y = 0 →
  39. 39.x + 4y = 5 and 4x + y = −10 →
  40. 40.4x − y = 25 and x − 2y = 15 →

Answer key

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

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