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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 867 · 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 = 12 and 4x + y = 4 →
  2. 2.6x + 4y = 42 and 5x + 2y = 27 →
  3. 3.6x + 4y = −26 and 5x − y = 13 →
  4. 4.6x − y = 10 and 2x − 5y = −6 →
  5. 5.2x + 4y = −54 and x + 3y = −36 →
  6. 6.4x + 6y = 36 and x + 3y = 12 →
  7. 7.x + 3y = −16 and 3x + y = 8 →
  8. 8.x − 5y = −52 and 2x + 3y = 13 →
  9. 9.2x − y = 10 and 6x + 3y = 18 →
  10. 10.4x + y = 37 and 3x − y = 12 →
  11. 11.3x + 7y = 28 and 7x + 3y = −28 →
  12. 12.x + 4y = 11 and 2x − y = −23 →
  13. 13.x − 5y = −42 and 5x − 6y = −58 →
  14. 14.2x − 2y = 4 and 5x + y = −20 →
  15. 15.6x + 6y = 60 and 5x + y = 38 →
  16. 16.4x + 7y = −59 and 7x + 4y = −29 →
  17. 17.6x + 6y = 96 and x − y = 0 →
  18. 18.3x + 5y = −66 and 2x + 2y = −32 →
  19. 19.2x − 4y = −16 and x − 6y = −40 →
  20. 20.2x + 4y = 38 and 4x + 2y = 40 →
  21. 21.2x + 3y = 14 and 3x − 2y = −5 →
  22. 22.3x + 2y = 2 and 6x + 6y = 0 →
  23. 23.2x + y = 18 and 3x + y = 23 →
  24. 24.2x + 6y = 18 and 6x + y = 37 →
  25. 25.x + 2y = 15 and x − 4y = −39 →
  26. 26.4x + 6y = −10 and 4x − 6y = −22 →
  27. 27.4x + 7y = −31 and 7x + 4y = −46 →
  28. 28.x + 6y = 12 and 6x + y = 37 →
  29. 29.3x + 4y = 34 and 4x + 3y = 29 →
  30. 30.2x + y = −7 and 2x − y = 3 →
  31. 31.3x + 5y = −2 and x + y = 2 →
  32. 32.x + 4y = 13 and 2x − 3y = −7 →
  33. 33.x − 3y = 12 and x + y = 8 →
  34. 34.2x + y = 11 and x + 2y = 4 →
  35. 35.7x + 8y = 30 and 8x + 7y = 30 →
  36. 36.8x + 3y = 56 and 3x + 8y = 76 →
  37. 37.4x + 5y = −12 and 5x + 4y = −24 →
  38. 38.6x − 2y = 0 and 2x + 6y = 20 →
  39. 39.2x − 4y = −36 and 6x + 5y = 28 →
  40. 40.x + 6y = 44 and 2x + 4y = 32 →

Answer key

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

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