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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 388 · 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. 1.9x + 5y = −70 and 5x + 9y = −70 →
  2. 2.x − 3y = 0 and 4x + 2y = 28 →
  3. 3.4x + 2y = −52 and 6x − 3y = −30 →
  4. 4.2x + y = −19 and 4x + 6y = −58 →
  5. 5.6x + 4y = −12 and 4x + 6y = −28 →
  6. 6.3x + 3y = 27 and x + 6y = 29 →
  7. 7.3x − 2y = 29 and 5x − 4y = 51 →
  8. 8.x + 2y = −22 and 5x − 6y = 34 →
  9. 9.3x + 3y = 27 and 6x − 4y = 24 →
  10. 10.6x + 4y = −12 and 4x + 6y = 12 →
  11. 11.3x + 6y = −36 and 3x + 2y = −8 →
  12. 12.6x + 4y = −2 and 2x + 6y = 32 →
  13. 13.6x + 3y = −6 and 3x + 6y = −21 →
  14. 14.6x + 9y = 21 and 9x + 6y = 24 →
  15. 15.4x + 7y = 30 and 7x + 4y = 3 →
  16. 16.3x + y = 9 and x + 3y = 19 →
  17. 17.3x + 5y = 13 and 5x + 3y = 27 →
  18. 18.4x + 6y = 30 and 2x + 4y = 14 →
  19. 19.5x + 4y = −29 and 2x + 6y = −38 →
  20. 20.6x + 5y = 72 and 5x + 6y = 71 →
  21. 21.2x + 2y = 2 and x − y = −7 →
  22. 22.5x + 7y = −55 and 7x + 5y = −53 →
  23. 23.2x + 6y = −44 and 6x + 2y = −52 →
  24. 24.4x − 3y = 47 and 4x + 5y = −25 →
  25. 25.5x − 3y = −49 and 6x + 5y = −33 →
  26. 26.4x + 7y = 37 and 7x + 4y = 7 →
  27. 27.x − y = −4 and 4x + y = −11 →
  28. 28.5x − 3y = −3 and 4x − 2y = 0 →
  29. 29.5x + y = 12 and 3x − 4y = −25 →
  30. 30.3x + 3y = 15 and 4x + 2y = 12 →
  31. 31.6x + 8y = −14 and 8x + 6y = −42 →
  32. 32.6x + 4y = −26 and 4x + 6y = 6 →
  33. 33.5x − 2y = 19 and 6x − 3y = 24 →
  34. 34.3x + y = 6 and x + 6y = 19 →
  35. 35.2x − 5y = 6 and x − 3y = 2 →
  36. 36.4x + 4y = 4 and 2x − y = −22 →
  37. 37.x − y = −7 and 3x + 6y = −30 →
  38. 38.6x + 5y = 1 and 5x + 6y = −1 →
  39. 39.9x + 4y = 49 and 4x + 9y = 29 →
  40. 40.5x + 2y = 19 and 2x + 5y = −5 →

Answer key

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

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