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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 764 · 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. 1.3x + y = 4 and x + 3y = −20 →
  2. 2.3x + 9y = 78 and 9x + 3y = 42 →
  3. 3.3x + y = −22 and 2x + 5y = −19 →
  4. 4.4x + 2y = 28 and x + 5y = −11 →
  5. 5.3x + 2y = −9 and x + y = 0 →
  6. 6.6x + 5y = −34 and 5x + 6y = −43 →
  7. 7.6x + 3y = −21 and 5x − 6y = −26 →
  8. 8.3x + 2y = −22 and 3x + 3y = −21 →
  9. 9.x + 2y = −9 and 2x + 3y = −10 →
  10. 10.x + 6y = 35 and 6x + y = 35 →
  11. 11.5x + 3y = 14 and 3x + 2y = 9 →
  12. 12.3x + y = 7 and 2x + 3y = 7 →
  13. 13.2x + 9y = −7 and 9x + 2y = 7 →
  14. 14.8x + 4y = −60 and 4x + 8y = −36 →
  15. 15.6x − 4y = 2 and x + 2y = 3 →
  16. 16.3x + y = 20 and x + 3y = −12 →
  17. 17.x + 2y = 8 and 4x − 4y = 8 →
  18. 18.2x + 5y = 41 and 5x + 2y = 8 →
  19. 19.4x + 7y = −53 and 7x + 4y = −35 →
  20. 20.5x + 2y = 24 and 2x + 5y = −3 →
  21. 21.9x + 2y = 38 and 2x + 9y = 17 →
  22. 22.x + 2y = −9 and 2x + y = −12 →
  23. 23.5x + 2y = 51 and x − 2y = 3 →
  24. 24.9x + 2y = −32 and 2x + 9y = 10 →
  25. 25.5x + 8y = 43 and 8x + 5y = 61 →
  26. 26.2x − 6y = 22 and x + 4y = −24 →
  27. 27.3x + y = 27 and 3x + 3y = 45 →
  28. 28.4x − 2y = −14 and x + 5y = −31 →
  29. 29.3x + 2y = 25 and 2x + 3y = 20 →
  30. 30.2x + y = −7 and x + 2y = 7 →
  31. 31.4x + 2y = 6 and 2x + 6y = 38 →
  32. 32.x + 5y = −42 and 4x + 3y = −15 →
  33. 33.5x + 3y = −10 and 5x − 2y = −35 →
  34. 34.x + 2y = 0 and 2x + y = 3 →
  35. 35.x + 2y = 8 and 2x + y = 10 →
  36. 36.4x + 2y = 54 and 2x + 4y = 54 →
  37. 37.x + 6y = −45 and 3x + 4y = −51 →
  38. 38.x − 3y = 28 and 5x + y = −4 →
  39. 39.2x + 2y = 4 and 4x + 6y = −2 →
  40. 40.2x + 6y = 42 and 5x + y = 35 →

Answer key

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

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