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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 204 · 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 + 4y = 12 and 4x + 8y = 0 →
  2. 2.6x + 3y = 12 and 5x + 6y = −11 →
  3. 3.4x + 5y = −2 and x + 3y = 3 →
  4. 4.3x + 4y = −26 and 2x − 4y = −4 →
  5. 5.4x + 9y = −62 and 9x + 4y = −42 →
  6. 6.5x + y = 22 and x + 3y = 24 →
  7. 7.2x − y = −11 and x − y = −6 →
  8. 8.5x + 2y = −24 and 2x + 5y = −39 →
  9. 9.9x + y = −47 and x + 9y = −23 →
  10. 10.x + 8y = 63 and 8x + y = 63 →
  11. 11.3x − 2y = 13 and 2x − y = 10 →
  12. 12.4x + 9y = 0 and 9x + 4y = 65 →
  13. 13.8x + 4y = −4 and 4x + 8y = 16 →
  14. 14.2x + 3y = 24 and 2x + 5y = 36 →
  15. 15.x − 3y = 17 and 5x − 5y = 45 →
  16. 16.3x + 6y = −54 and 6x + 3y = −36 →
  17. 17.2x − 2y = 8 and 3x + 3y = 24 →
  18. 18.x + 2y = 1 and 6x + 6y = 0 →
  19. 19.x + 8y = −26 and 8x + y = 44 →
  20. 20.x − 3y = −4 and x + 5y = 20 →
  21. 21.x − 3y = −10 and x + 3y = 2 →
  22. 22.x + 6y = −23 and 2x + 2y = 4 →
  23. 23.x − 3y = −10 and 5x − y = 20 →
  24. 24.4x + 5y = −1 and 4x + 4y = 4 →
  25. 25.2x + 5y = 9 and 5x + 2y = 12 →
  26. 26.6x − 6y = 6 and 2x + 2y = 10 →
  27. 27.6x + 4y = −90 and 6x + y = −63 →
  28. 28.3x + 8y = 28 and 8x + 3y = −17 →
  29. 29.x − 3y = −9 and 3x − 3y = 9 →
  30. 30.x + 3y = 26 and 3x + y = 30 →
  31. 31.2x + 5y = 15 and 4x − 4y = −40 →
  32. 32.x + 6y = −11 and x + 3y = −5 →
  33. 33.5x + 5y = 5 and 2x − 3y = 42 →
  34. 34.2x − 3y = 5 and 5x + 2y = 3 →
  35. 35.8x + 7y = 72 and 7x + 8y = 78 →
  36. 36.6x + 5y = 41 and 5x + 6y = 36 →
  37. 37.8x + 6y = 94 and 6x + 8y = 102 →
  38. 38.5x + 3y = 52 and 4x + 4y = 56 →
  39. 39.4x − 6y = −38 and x + 5y = 10 →
  40. 40.6x − 3y = −21 and 3x − 3y = −24 →

Answer key

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

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