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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 840 · 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 + 5y = −43 and 4x − y = −1 →
  2. 2.3x − y = 18 and 5x + y = 38 →
  3. 3.x + 3y = 2 and 3x + y = −2 →
  4. 4.4x + 2y = 32 and 2x + 3y = 24 →
  5. 5.2x + 4y = −6 and 4x + 2y = 0 →
  6. 6.6x − 5y = 22 and 5x + 3y = 4 →
  7. 7.5x + 5y = 30 and x − 2y = −3 →
  8. 8.3x − 5y = 7 and x + y = 5 →
  9. 9.2x + 5y = −7 and 5x + 2y = 14 →
  10. 10.2x + y = 11 and 3x − 4y = −22 →
  11. 11.6x + 5y = 70 and 6x + 6y = 78 →
  12. 12.x + y = 10 and 2x + 5y = 38 →
  13. 13.6x − 5y = −21 and x + 3y = 31 →
  14. 14.x + y = 1 and 5x + 3y = 15 →
  15. 15.x + 8y = −39 and 8x + y = −60 →
  16. 16.2x + y = 5 and x − 2y = −5 →
  17. 17.3x − y = 14 and 4x + 6y = 70 →
  18. 18.x − 2y = −4 and 4x + y = 20 →
  19. 19.2x + 3y = 39 and x + 5y = 44 →
  20. 20.2x + 6y = 50 and 2x + 3y = 26 →
  21. 21.2x + 2y = 10 and 2x + 5y = 7 →
  22. 22.x − 2y = −16 and 2x + 6y = 38 →
  23. 23.x + 4y = −13 and 4x + y = 8 →
  24. 24.2x + y = −4 and 5x + 5y = 0 →
  25. 25.4x + 3y = 31 and 5x − y = −4 →
  26. 26.x + 2y = 7 and x + 5y = 25 →
  27. 27.6x + 2y = 4 and 2x + 6y = −4 →
  28. 28.x + 2y = 15 and 2x + y = 21 →
  29. 29.2x + 9y = −13 and 9x + 2y = −20 →
  30. 30.6x − 4y = −46 and 3x + y = −20 →
  31. 31.6x + 3y = 66 and 4x + 5y = 68 →
  32. 32.2x − 2y = −16 and x + 4y = 2 →
  33. 33.2x + 2y = −12 and 6x + 4y = −38 →
  34. 34.2x + 3y = 24 and 2x − 3y = −12 →
  35. 35.2x + 5y = 27 and x + 2y = 11 →
  36. 36.x + y = −1 and 4x + y = −22 →
  37. 37.3x + 4y = 35 and 5x − y = 20 →
  38. 38.x − y = 7 and 5x − 2y = 23 →
  39. 39.2x + 6y = 32 and 6x − 4y = −14 →
  40. 40.6x + 4y = −60 and 3x − 4y = 24 →

Answer key

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

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