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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 208 · 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 + 6y = −45 and 3x + y = 18 →
  2. 2.2x + 4y = −12 and 2x + y = −15 →
  3. 3.x − 6y = −7 and 2x + 5y = 20 →
  4. 4.4x + 3y = 14 and 3x + 4y = 14 →
  5. 5.3x + y = 20 and 5x + y = 30 →
  6. 6.x + 8y = −32 and 8x + y = 59 →
  7. 7.4x + 9y = −45 and 9x + 4y = 45 →
  8. 8.4x + 9y = −70 and 9x + 4y = −60 →
  9. 9.5x − 4y = 15 and 3x + y = −8 →
  10. 10.6x − 2y = −24 and 5x + 3y = 22 →
  11. 11.2x + 4y = 10 and 4x + 2y = −22 →
  12. 12.6x + 4y = 12 and 4x + 6y = 28 →
  13. 13.3x + 5y = −19 and 5x + 6y = −13 →
  14. 14.x + 2y = −7 and 2x + y = −2 →
  15. 15.2x + y = −8 and x + 3y = 6 →
  16. 16.6x + y = 2 and x + 6y = 47 →
  17. 17.8x + 7y = 10 and 7x + 8y = 5 →
  18. 18.5x + 9y = 43 and 9x + 5y = −1 →
  19. 19.4x + 2y = −34 and 4x − 4y = −4 →
  20. 20.2x + 7y = 42 and 7x + 2y = 57 →
  21. 21.6x + 5y = 32 and 5x + 5y = 30 →
  22. 22.2x + 2y = −4 and 4x + 3y = −13 →
  23. 23.3x + y = −11 and 5x + 5y = 5 →
  24. 24.4x + 5y = −12 and 5x + 2y = 2 →
  25. 25.4x − y = 27 and x − 4y = 3 →
  26. 26.5x + 3y = 48 and 3x + 5y = 32 →
  27. 27.7x + y = 43 and x + 7y = 61 →
  28. 28.6x + 5y = −41 and 5x + 6y = −47 →
  29. 29.6x + 4y = −12 and 2x + 5y = 18 →
  30. 30.4x − 3y = 4 and 2x + y = 12 →
  31. 31.8x + 2y = 12 and 2x + 8y = 18 →
  32. 32.x + 3y = 1 and 3x + y = −5 →
  33. 33.x + y = 11 and 6x + y = 46 →
  34. 34.6x + 2y = 68 and 6x + 4y = 82 →
  35. 35.3x − 6y = −36 and 6x + 4y = −8 →
  36. 36.2x + y = −6 and x − y = 9 →
  37. 37.3x + 4y = −48 and 4x − y = −26 →
  38. 38.5x + 2y = 12 and x + 5y = −39 →
  39. 39.x + 2y = −10 and 4x − 2y = 30 →
  40. 40.4x + 8y = −20 and 8x + 4y = −16 →

Answer key

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

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