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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 621 · 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. 1.8x + 5y = 29 and 5x + 8y = 23 →
  2. 2.7x + 9y = 33 and 9x + 7y = 15 →
  3. 3.6x + 2y = −58 and 2x + 5y = −54 →
  4. 4.2x + 3y = −30 and 3x + 2y = −35 →
  5. 5.5x + 6y = 87 and 5x + 4y = 73 →
  6. 6.6x + y = −11 and 2x + 2y = 8 →
  7. 7.x + 3y = −5 and 3x + 4y = −20 →
  8. 8.2x − y = −19 and x + 6y = 10 →
  9. 9.6x + 9y = 27 and 9x + 6y = 3 →
  10. 10.5x + 6y = 61 and 6x + 5y = 60 →
  11. 11.5x + 4y = −36 and 4x + 5y = −27 →
  12. 12.x + 3y = 13 and x + 6y = 25 →
  13. 13.3x + 2y = 17 and 2x + 2y = 10 →
  14. 14.6x − 3y = −27 and 2x − 4y = 0 →
  15. 15.6x + 2y = 44 and x + 2y = 19 →
  16. 16.6x + 2y = 70 and 2x + 2y = 34 →
  17. 17.x + 4y = 24 and 5x + 3y = 52 →
  18. 18.5x − 4y = 41 and 6x − y = 15 →
  19. 19.8x + y = 59 and x + 8y = 31 →
  20. 20.4x + 6y = 6 and 5x + 6y = −3 →
  21. 21.x + 2y = 3 and 5x + 5y = 25 →
  22. 22.4x + y = 28 and 3x − 2y = 10 →
  23. 23.4x − 6y = −4 and 5x − 6y = −2 →
  24. 24.2x − 4y = −10 and 2x − 2y = 2 →
  25. 25.4x − 5y = −51 and 2x − y = −21 →
  26. 26.4x + 4y = −40 and 5x + 6y = −51 →
  27. 27.x + 3y = 26 and 3x + y = 30 →
  28. 28.x + 2y = −1 and 2x + 2y = 2 →
  29. 29.6x + 8y = 30 and 8x + 6y = 12 →
  30. 30.3x − 5y = 2 and 3x + 3y = 42 →
  31. 31.5x − 2y = −55 and 5x + y = −40 →
  32. 32.x − 5y = −22 and 2x − 4y = −8 →
  33. 33.3x + 9y = −36 and 9x + 3y = −84 →
  34. 34.2x − 3y = 29 and 3x + 2y = −2 →
  35. 35.2x + 9y = 88 and 9x + 2y = 88 →
  36. 36.8x + 6y = −30 and 6x + 8y = −54 →
  37. 37.2x + 3y = 14 and 5x − 3y = −7 →
  38. 38.3x + 4y = 7 and 5x + 2y = 7 →
  39. 39.4x + 4y = 20 and 2x + 3y = 19 →
  40. 40.6x − 2y = 66 and 6x − 5y = 84 →

Answer key

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

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