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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 430 · 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 + 2y = 0 and 3x + 5y = 14 →
  2. 2.3x + 6y = 51 and 6x + 3y = 57 →
  3. 3.5x + 3y = 8 and 3x + 5y = 8 →
  4. 4.x − 6y = −16 and 2x + 5y = 2 →
  5. 5.3x + 2y = 13 and x + y = 4 →
  6. 6.2x + y = −3 and 3x + 3y = −6 →
  7. 7.2x − y = 7 and 4x − y = 19 →
  8. 8.5x − 4y = 16 and 6x − 5y = 19 →
  9. 9.2x + 3y = 7 and 3x + 2y = 8 →
  10. 10.9x + 7y = −51 and 7x + 9y = −29 →
  11. 11.4x − 3y = 0 and x − y = −1 →
  12. 12.x + 9y = −38 and 9x + y = −22 →
  13. 13.5x − 4y = −49 and 6x + 5y = −49 →
  14. 14.5x + 3y = 39 and x + 5y = 43 →
  15. 15.4x + y = 0 and x + 4y = −30 →
  16. 16.4x + 9y = 25 and 9x + 4y = 40 →
  17. 17.4x − 2y = 44 and 3x + 2y = 5 →
  18. 18.2x + 3y = 13 and 6x − y = 49 →
  19. 19.x + 7y = 20 and 7x + y = −4 →
  20. 20.2x − 4y = −16 and 5x + 3y = 51 →
  21. 21.3x + 9y = 96 and 9x + 3y = 72 →
  22. 22.3x + 8y = −34 and 8x + 3y = −54 →
  23. 23.2x + 5y = 3 and 4x + 4y = −12 →
  24. 24.3x + y = −20 and x + y = −8 →
  25. 25.3x − y = −12 and 4x + y = −2 →
  26. 26.x + 6y = 29 and 2x + y = 3 →
  27. 27.6x − 5y = −24 and 4x + y = 10 →
  28. 28.8x + 3y = −57 and 3x + 8y = 13 →
  29. 29.8x + 6y = 10 and 6x + 8y = 4 →
  30. 30.6x − 5y = 70 and 2x − 2y = 26 →
  31. 31.7x + 8y = −7 and 8x + 7y = −23 →
  32. 32.7x + y = 50 and x + 7y = −34 →
  33. 33.x + 3y = −21 and 5x + 4y = −17 →
  34. 34.x + y = −3 and 6x − 4y = −38 →
  35. 35.2x + 3y = 25 and 3x + 2y = 20 →
  36. 36.2x + 4y = −6 and 3x + 5y = −3 →
  37. 37.6x + 5y = −13 and 3x + 6y = 18 →
  38. 38.2x + 4y = 40 and 6x − y = 42 →
  39. 39.3x + y = 24 and 5x + y = 38 →
  40. 40.x − y = −17 and 6x + y = −46 →

Answer key

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

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