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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 269 · 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 = 11 and 6x + 5y = 0 →
  2. 2.3x + 5y = −6 and 5x + 3y = −26 →
  3. 3.4x − 2y = −2 and 4x + 3y = 23 →
  4. 4.x − 5y = −11 and 2x + 4y = 34 →
  5. 5.2x + 3y = 22 and 2x + 5y = 26 →
  6. 6.2x + 2y = −10 and 6x + 2y = −46 →
  7. 7.6x + 5y = −22 and 4x + 4y = −20 →
  8. 8.4x + 3y = 30 and 6x + 2y = 50 →
  9. 9.2x − 6y = −10 and 2x + 5y = 12 →
  10. 10.x + 2y = −15 and 5x + 2y = −19 →
  11. 11.4x + 2y = 38 and 2x + 4y = 46 →
  12. 12.x + 3y = 10 and 4x − 6y = 22 →
  13. 13.6x − 6y = 54 and x − 2y = 17 →
  14. 14.3x + 2y = 24 and 2x + 3y = 31 →
  15. 15.5x + 7y = −9 and 7x + 5y = −3 →
  16. 16.x − 3y = −14 and 3x + 6y = −12 →
  17. 17.3x − y = −17 and x − 3y = −11 →
  18. 18.6x + 3y = 12 and x − 6y = 54 →
  19. 19.x − 4y = −7 and 2x − 6y = −6 →
  20. 20.4x − y = 25 and 4x + y = 7 →
  21. 21.6x + 9y = 69 and 9x + 6y = 66 →
  22. 22.4x + 2y = 34 and 2x + 4y = 20 →
  23. 23.6x + 4y = −50 and 6x − 2y = −2 →
  24. 24.6x − y = 53 and 6x + 5y = 59 →
  25. 25.x + 5y = 18 and 5x + y = 18 →
  26. 26.6x + 2y = −28 and 6x + 6y = −24 →
  27. 27.4x − 2y = 14 and 6x + 3y = 3 →
  28. 28.2x + 7y = 33 and 7x + 2y = 3 →
  29. 29.x − 5y = 13 and 4x + 4y = 28 →
  30. 30.2x + 6y = 38 and 6x − 3y = −75 →
  31. 31.3x − 2y = 11 and 4x + 2y = −4 →
  32. 32.5x + 6y = −22 and 3x + y = 5 →
  33. 33.7x + 5y = 78 and 5x + 7y = 66 →
  34. 34.6x + y = 31 and 3x + y = 16 →
  35. 35.3x + y = −33 and 6x − 4y = −12 →
  36. 36.3x − 3y = 12 and 2x + 5y = 43 →
  37. 37.8x + 3y = 43 and 3x + 8y = −32 →
  38. 38.5x + 3y = −36 and 2x − 4y = −30 →
  39. 39.3x + 3y = 39 and 5x + 3y = 57 →
  40. 40.4x + 2y = 16 and 2x + 3y = 4 →

Answer key

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

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