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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 308 · 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. 1.2x − 6y = −28 and 6x + 2y = 36 →
  2. 2.6x + 2y = 8 and 6x + 4y = 4 →
  3. 3.6x + 5y = −10 and 4x + 2y = −12 →
  4. 4.4x + 6y = −56 and x − 4y = 19 →
  5. 5.8x + 5y = −29 and 5x + 8y = −23 →
  6. 6.4x + 7y = −36 and 7x + 4y = −30 →
  7. 7.6x − y = 11 and 3x − y = 5 →
  8. 8.5x + 3y = 18 and 3x + 5y = −2 →
  9. 9.6x − 6y = −30 and x + 6y = 9 →
  10. 10.x + y = −11 and x − 6y = 31 →
  11. 11.3x + y = 4 and x + 3y = 4 →
  12. 12.4x + y = 23 and x + 4y = 2 →
  13. 13.6x + 6y = −24 and 6x − 6y = 36 →
  14. 14.6x − 4y = 62 and x − 2y = 17 →
  15. 15.x − 3y = 32 and 5x + 3y = −2 →
  16. 16.2x + 8y = −42 and 8x + 2y = 42 →
  17. 17.x + 2y = −4 and 4x + y = −23 →
  18. 18.6x + y = 58 and 2x + 4y = 34 →
  19. 19.4x + 4y = 24 and x + 2y = 15 →
  20. 20.2x + 9y = 3 and 9x + 2y = 52 →
  21. 21.4x + 6y = 42 and 4x + y = −3 →
  22. 22.5x + 4y = 35 and x + 6y = 33 →
  23. 23.5x + 6y = 31 and x − 4y = 1 →
  24. 24.x + 3y = 15 and 2x − 4y = −40 →
  25. 25.6x + 8y = −4 and 8x + 6y = 4 →
  26. 26.7x + 2y = 13 and 2x + 7y = 23 →
  27. 27.6x − 5y = −58 and 5x + 6y = 33 →
  28. 28.x + 2y = 14 and 2x + y = 4 →
  29. 29.2x − 4y = −24 and 6x + 6y = −36 →
  30. 30.2x + 4y = −14 and 3x + 3y = −9 →
  31. 31.8x + 5y = 26 and 5x + 8y = 26 →
  32. 32.3x − 6y = 33 and 3x − 5y = 27 →
  33. 33.2x + 5y = 25 and 2x − 6y = −8 →
  34. 34.6x + 9y = 6 and 9x + 6y = 24 →
  35. 35.5x + 5y = 5 and 5x − 2y = 54 →
  36. 36.6x + 2y = 24 and 2x + 6y = 24 →
  37. 37.4x + y = −13 and x + 4y = 8 →
  38. 38.8x + 3y = 22 and 3x + 8y = −33 →
  39. 39.5x − 6y = −2 and x + 2y = 6 →
  40. 40.3x + 2y = 30 and 2x + 5y = 42 →

Answer key

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

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