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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 757 · 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 + 3y = −8 and 4x − y = −24 →
  2. 2.2x + 4y = −36 and 6x + 5y = −59 →
  3. 3.3x + y = 23 and 3x + 6y = 33 →
  4. 4.6x + 3y = 42 and 2x + 2y = 18 →
  5. 5.3x + 3y = −3 and 3x − 6y = −39 →
  6. 6.3x + 5y = 44 and 6x − 2y = 40 →
  7. 7.9x + 4y = 13 and 4x + 9y = 13 →
  8. 8.2x − 2y = 8 and 3x − 5y = 22 →
  9. 9.7x + 2y = 35 and 2x + 7y = −35 →
  10. 10.x + 3y = −2 and 5x + 2y = −36 →
  11. 11.3x − 2y = −19 and 6x + 4y = 26 →
  12. 12.x − 6y = −29 and 3x + 5y = 5 →
  13. 13.4x + y = 16 and 2x + 6y = 30 →
  14. 14.x + 4y = −5 and 4x + 5y = −31 →
  15. 15.9x + 2y = −65 and 2x + 9y = 54 →
  16. 16.x + y = 17 and x + 4y = 44 →
  17. 17.4x + 2y = −34 and 3x + 2y = −25 →
  18. 18.x + 2y = 21 and 2x + y = 15 →
  19. 19.5x + y = −36 and 3x + 2y = −16 →
  20. 20.2x + 2y = −22 and 2x + 5y = −31 →
  21. 21.3x − 2y = 23 and 3x + 2y = 31 →
  22. 22.7x + 3y = 28 and 3x + 7y = 52 →
  23. 23.x + 2y = −1 and x − 4y = −13 →
  24. 24.4x + 6y = 18 and 6x − 3y = −81 →
  25. 25.8x + 5y = 38 and 5x + 8y = 53 →
  26. 26.7x + 3y = −18 and 3x + 7y = −2 →
  27. 27.x − 3y = 1 and 4x + 2y = 32 →
  28. 28.8x + 5y = −39 and 5x + 8y = −39 →
  29. 29.4x + 2y = 24 and 2x + 4y = 36 →
  30. 30.2x − 2y = −16 and 6x − 4y = −44 →
  31. 31.9x + 4y = 40 and 4x + 9y = −40 →
  32. 32.5x + 3y = −48 and x + 4y = −13 →
  33. 33.4x − 5y = 5 and x − y = 2 →
  34. 34.9x + 4y = 49 and 4x + 9y = −36 →
  35. 35.6x + y = 11 and x + 6y = −39 →
  36. 36.2x + 7y = 20 and 7x + 2y = 25 →
  37. 37.8x + 7y = −72 and 7x + 8y = −78 →
  38. 38.2x − 3y = −32 and 3x − 2y = −28 →
  39. 39.5x + y = 23 and 3x + 4y = 24 →
  40. 40.6x + 4y = −52 and 4x + 6y = −38 →

Answer key

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

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