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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 276 · 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 = 6 and 2x + 4y = 30 →
  2. 2.4x − 3y = −14 and x − y = −3 →
  3. 3.5x + 2y = 57 and 2x + 5y = 48 →
  4. 4.5x + 8y = −36 and 8x + 5y = −42 →
  5. 5.3x − y = 2 and 6x + y = 16 →
  6. 6.9x + 8y = 144 and 8x + 9y = 145 →
  7. 7.3x + 3y = −48 and 5x − 3y = −24 →
  8. 8.5x + 4y = 17 and 5x − y = 2 →
  9. 9.9x + 2y = −46 and 2x + 9y = 24 →
  10. 10.x − y = −11 and 6x − y = −36 →
  11. 11.6x + 5y = 45 and x + y = 8 →
  12. 12.x + 3y = −19 and 5x + 5y = −25 →
  13. 13.3x + 7y = −53 and 7x + 3y = −17 →
  14. 14.3x − 3y = 33 and 2x + 4y = 10 →
  15. 15.5x + 5y = −55 and x + 4y = −23 →
  16. 16.7x + y = −65 and x + 7y = −23 →
  17. 17.5x + 4y = 51 and 6x − y = 38 →
  18. 18.2x + 3y = 2 and 6x + 2y = −36 →
  19. 19.2x + 6y = −38 and 4x + y = 12 →
  20. 20.8x + 4y = 52 and 4x + 8y = 80 →
  21. 21.4x − 6y = 32 and 4x + 6y = 8 →
  22. 22.3x + 3y = 27 and 4x + 5y = 44 →
  23. 23.2x − y = 17 and 6x − 5y = 61 →
  24. 24.5x + 6y = 69 and 3x + 5y = 54 →
  25. 25.5x − 4y = −14 and 3x + 4y = −2 →
  26. 26.7x + 2y = 47 and 2x + 7y = 7 →
  27. 27.5x + y = 37 and x + 5y = 17 →
  28. 28.3x + 2y = 12 and 2x + 3y = 23 →
  29. 29.3x − 3y = 3 and 4x + 3y = 32 →
  30. 30.5x + 6y = 76 and 2x − 3y = −2 →
  31. 31.5x + 4y = 33 and 4x + 5y = 21 →
  32. 32.6x − 6y = −12 and x + 6y = 47 →
  33. 33.3x + 2y = 14 and 6x + 2y = 20 →
  34. 34.5x − 6y = −69 and 4x + y = −3 →
  35. 35.3x + y = −2 and 3x − 6y = 54 →
  36. 36.2x + 9y = 11 and 9x + 2y = 11 →
  37. 37.5x + 2y = −26 and 6x + 3y = −36 →
  38. 38.7x + 2y = 30 and 2x + 7y = 60 →
  39. 39.5x − 3y = −20 and x − 6y = −31 →
  40. 40.6x − y = 33 and 4x − 3y = 29 →

Answer key

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

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