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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 435 · 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 + 7y = −73 and 7x + 2y = −53 →
  2. 2.6x + 8y = 40 and 8x + 6y = 58 →
  3. 3.6x + 8y = −22 and 8x + 6y = −34 →
  4. 4.x + 3y = 9 and 3x + y = 11 →
  5. 5.5x + 2y = 17 and x − 6y = −3 →
  6. 6.5x + 5y = 35 and 3x + y = 25 →
  7. 7.4x − 6y = 22 and 2x + 3y = −43 →
  8. 8.3x + y = −5 and 3x + 3y = 3 →
  9. 9.x + 3y = −9 and 4x + 6y = −6 →
  10. 10.x + 3y = 17 and 3x + y = −13 →
  11. 11.5x + 4y = −36 and 4x + 2y = −30 →
  12. 12.6x − 5y = 99 and x − 6y = 63 →
  13. 13.6x + 6y = 60 and 5x + y = 34 →
  14. 14.5x + 6y = 7 and 6x + 5y = −7 →
  15. 15.2x + 8y = 70 and 8x + 2y = 10 →
  16. 16.6x − y = −51 and 4x + 5y = −51 →
  17. 17.4x + y = 9 and x + 4y = −9 →
  18. 18.x − y = 2 and x − 2y = −5 →
  19. 19.x + 3y = 6 and 3x + y = 10 →
  20. 20.4x + 3y = −30 and 3x + 4y = −26 →
  21. 21.4x + 3y = 15 and 4x − 3y = 33 →
  22. 22.5x + 3y = −13 and 3x + 5y = 21 →
  23. 23.3x + 3y = 0 and 4x + y = −3 →
  24. 24.x − 5y = −36 and 5x + 3y = 16 →
  25. 25.9x + 2y = −60 and 2x + 9y = 38 →
  26. 26.5x + 3y = 10 and 2x + 2y = 0 →
  27. 27.6x + 3y = 60 and 3x + 6y = 57 →
  28. 28.4x − y = 34 and 6x + 3y = 42 →
  29. 29.2x − 4y = 20 and 3x + 6y = −6 →
  30. 30.x − y = 2 and 4x − 6y = 0 →
  31. 31.5x − 4y = −53 and 5x + 4y = −37 →
  32. 32.2x + 7y = −38 and 7x + 2y = 47 →
  33. 33.2x − 2y = −8 and 2x − 4y = −20 →
  34. 34.x − 2y = 16 and 3x + 2y = −8 →
  35. 35.3x − 5y = −69 and x − 5y = −53 →
  36. 36.4x + 2y = 4 and 5x + 6y = 33 →
  37. 37.x + 2y = −18 and 2x + y = −15 →
  38. 38.x + y = −1 and 4x − 4y = −36 →
  39. 39.5x + 6y = −60 and 6x + 5y = −61 →
  40. 40.4x − 3y = −20 and 5x − 4y = −27 →

Answer key

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

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