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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 188 · 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. 1.4x − 2y = 2 and x + 6y = 33 →
  2. 2.x + y = 3 and 5x + y = 19 →
  3. 3.2x + y = 14 and x + 2y = 19 →
  4. 4.3x + 4y = 53 and 4x + 3y = 52 →
  5. 5.x + 8y = −47 and 8x + y = 2 →
  6. 6.x − 3y = −16 and 2x + 2y = 16 →
  7. 7.2x + 2y = 18 and 4x − 4y = −20 →
  8. 8.5x − 4y = 46 and 5x − y = 19 →
  9. 9.x + 2y = −17 and 2x + y = −22 →
  10. 10.x + 6y = 52 and 6x + y = −3 →
  11. 11.9x + 7y = 107 and 7x + 9y = 101 →
  12. 12.x + 3y = 17 and x − y = −15 →
  13. 13.3x + 2y = −1 and 3x + 3y = 0 →
  14. 14.3x + 7y = −36 and 7x + 3y = −4 →
  15. 15.7x + y = −16 and x + 7y = −16 →
  16. 16.4x − 6y = 84 and 5x + y = 37 →
  17. 17.4x + y = 41 and 6x − 5y = 29 →
  18. 18.5x + 6y = 4 and x + 4y = 12 →
  19. 19.5x + 2y = 14 and 4x + 5y = −16 →
  20. 20.x + 5y = 23 and 5x + y = 43 →
  21. 21.x + 4y = −20 and 4x + y = 25 →
  22. 22.5x + 3y = 19 and 2x + 4y = 30 →
  23. 23.2x + 5y = −11 and 5x + 2y = −38 →
  24. 24.2x + 8y = −28 and 8x + 2y = −22 →
  25. 25.9x + 6y = 3 and 6x + 9y = 12 →
  26. 26.3x − 6y = 21 and 4x − 2y = 16 →
  27. 27.2x − 4y = −2 and 4x − 4y = 0 →
  28. 28.x + 2y = −3 and x − 4y = −15 →
  29. 29.2x + 6y = −44 and 6x + 2y = −4 →
  30. 30.5x + y = −14 and 4x + 5y = −49 →
  31. 31.5x + y = 39 and x + 5y = 51 →
  32. 32.2x + 9y = 26 and 9x + 2y = 40 →
  33. 33.4x + y = 15 and 6x + 5y = 19 →
  34. 34.4x + y = −16 and 4x − y = −24 →
  35. 35.4x + 4y = 4 and 3x − 2y = −42 →
  36. 36.8x + 5y = −77 and 5x + 8y = −53 →
  37. 37.4x − 4y = 32 and 3x + 4y = 17 →
  38. 38.8x + 4y = 92 and 4x + 8y = 88 →
  39. 39.4x + y = −17 and x + 4y = −8 →
  40. 40.x + 2y = 11 and 4x + 6y = 32 →

Answer key

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

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