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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 13 · 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. 1.6x + 3y = 15 and 5x + y = 2 →
  2. 2.4x + 9y = −63 and 9x + 4y = −93 →
  3. 3.6x + 4y = 66 and 6x − 6y = 36 →
  4. 4.4x − 6y = 50 and 2x + 4y = −24 →
  5. 5.2x + 3y = 14 and 6x + y = −22 →
  6. 6.2x + 8y = −10 and 8x + 2y = 20 →
  7. 7.x − 2y = −2 and 6x − 5y = 9 →
  8. 8.6x − 4y = −36 and 6x + 3y = −15 →
  9. 9.3x + 9y = −3 and 9x + 3y = 15 →
  10. 10.x + 6y = 4 and 3x − 6y = −36 →
  11. 11.6x + 3y = 0 and 4x − y = 18 →
  12. 12.2x + 7y = −38 and 7x + 2y = 2 →
  13. 13.x + 4y = 8 and 4x + y = 17 →
  14. 14.8x + 6y = −102 and 6x + 8y = −94 →
  15. 15.4x + y = 30 and x + 4y = 15 →
  16. 16.9x + 2y = 55 and 2x + 9y = 55 →
  17. 17.3x − 4y = −52 and 4x + 4y = −4 →
  18. 18.5x + 3y = 29 and 2x + 5y = 23 →
  19. 19.3x + 2y = 1 and 3x − 6y = −39 →
  20. 20.6x + 6y = 54 and 4x − 5y = −18 →
  21. 21.2x + 3y = 0 and 5x + y = −26 →
  22. 22.2x − 4y = −36 and x + 4y = 12 →
  23. 23.7x + y = 27 and x + 7y = −51 →
  24. 24.x + 2y = 18 and 6x − 5y = 6 →
  25. 25.2x + 4y = −18 and 4x + 2y = 18 →
  26. 26.6x + y = 27 and 3x + 3y = 36 →
  27. 27.5x + 3y = 60 and 3x + 5y = 52 →
  28. 28.3x + 9y = 12 and 9x + 3y = 12 →
  29. 29.2x + 5y = 15 and x − 5y = 0 →
  30. 30.x − 5y = −12 and 5x + 5y = 0 →
  31. 31.6x + y = −14 and x + 6y = −49 →
  32. 32.3x + 5y = 63 and x − y = −3 →
  33. 33.5x + 9y = 60 and 9x + 5y = 52 →
  34. 34.6x − 6y = 66 and x + 3y = −9 →
  35. 35.x + 2y = −17 and x + 5y = −44 →
  36. 36.3x + 6y = 15 and 6x + y = 8 →
  37. 37.x − 2y = −3 and x − 6y = −11 →
  38. 38.5x + 6y = 36 and x + 4y = 10 →
  39. 39.7x + 9y = −64 and 9x + 7y = −64 →
  40. 40.6x + 3y = 33 and x − y = 7 →

Answer key

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

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