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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 684 · 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. 1.5x + 6y = 22 and x + y = 4 →
  2. 2.2x + 5y = −42 and 4x − 5y = 36 →
  3. 3.6x + 7y = 45 and 7x + 6y = 33 →
  4. 4.2x + 3y = −2 and 4x + 4y = 0 →
  5. 5.8x + 5y = −58 and 5x + 8y = −46 →
  6. 6.4x + 5y = 57 and 5x − 2y = −3 →
  7. 7.3x − 5y = −4 and 6x + y = −52 →
  8. 8.4x + 5y = 18 and 5x + 4y = 18 →
  9. 9.x + 4y = 18 and 6x + 6y = 36 →
  10. 10.5x + y = 13 and x + 5y = 17 →
  11. 11.6x + 3y = 30 and x − 5y = −17 →
  12. 12.2x + 3y = 25 and x − 6y = −25 →
  13. 13.2x − 2y = −14 and 6x − 3y = −18 →
  14. 14.x − 6y = −26 and 4x + 3y = 4 →
  15. 15.5x − 3y = 44 and 3x + 4y = 9 →
  16. 16.5x + 5y = 65 and 5x + 6y = 71 →
  17. 17.x + 2y = −15 and 4x + 6y = −46 →
  18. 18.x + 3y = 19 and 3x + y = 1 →
  19. 19.2x − 2y = 14 and x + 2y = 4 →
  20. 20.3x + 5y = −39 and 4x + 4y = −36 →
  21. 21.x + 9y = 81 and 9x + y = 89 →
  22. 22.6x − 3y = −45 and 5x − 4y = −36 →
  23. 23.6x + 7y = −44 and 7x + 6y = −34 →
  24. 24.5x + 4y = 53 and 4x + 5y = 55 →
  25. 25.6x − 5y = 26 and 6x + 2y = 40 →
  26. 26.2x + 6y = 36 and 2x − 5y = −63 →
  27. 27.2x − 6y = −50 and 2x − y = −10 →
  28. 28.5x + 2y = −30 and 3x + 2y = −22 →
  29. 29.5x − 6y = 42 and 4x + y = 22 →
  30. 30.5x − 2y = −37 and 3x + 3y = −18 →
  31. 31.3x − y = 21 and 5x + 6y = 12 →
  32. 32.x + 8y = −76 and 8x + y = −41 →
  33. 33.3x + y = 9 and 2x + y = 8 →
  34. 34.8x + 3y = −2 and 3x + 8y = −42 →
  35. 35.3x + 5y = 45 and x + 5y = 35 →
  36. 36.x + 8y = 22 and 8x + y = −13 →
  37. 37.x − 2y = 6 and 6x − y = −19 →
  38. 38.4x + 2y = 36 and 2x + 4y = 36 →
  39. 39.3x + 2y = 33 and 2x + 5y = 33 →
  40. 40.3x + 6y = 9 and 6x + 3y = 36 →

Answer key

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

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