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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 288 · 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. 1.3x + y = 26 and x + 3y = 30 →
  2. 2.5x + 3y = −31 and 3x + 5y = −9 →
  3. 3.2x + 3y = 42 and 3x + 2y = 43 →
  4. 4.5x − 5y = 30 and 5x + 6y = 41 →
  5. 5.3x + 6y = 24 and 2x − 4y = −8 →
  6. 6.5x + 5y = 20 and 4x − 5y = −38 →
  7. 7.2x − y = 8 and x − 5y = −5 →
  8. 8.7x + 5y = 43 and 5x + 7y = 17 →
  9. 9.x + 3y = 14 and 3x + y = 10 →
  10. 10.3x + y = 30 and 6x − 3y = 45 →
  11. 11.5x + 4y = 18 and 2x + 5y = 14 →
  12. 12.3x + 4y = 26 and 4x + 5y = 34 →
  13. 13.3x + 2y = −33 and 5x + 4y = −61 →
  14. 14.5x + 4y = −53 and 2x + 5y = −45 →
  15. 15.3x + 8y = −53 and 8x + 3y = −13 →
  16. 16.5x + 3y = 10 and 2x − 6y = 40 →
  17. 17.2x − y = −2 and 4x + 4y = 32 →
  18. 18.4x + y = −9 and 2x − 5y = 1 →
  19. 19.3x + y = 16 and 2x + 2y = 20 →
  20. 20.2x + 8y = 18 and 8x + 2y = 12 →
  21. 21.5x + 6y = 52 and x + 5y = 37 →
  22. 22.x − 2y = 5 and x + 3y = 10 →
  23. 23.6x − 2y = 24 and x + y = 8 →
  24. 24.6x + 4y = 18 and x + 5y = −23 →
  25. 25.5x + 4y = −5 and 4x + 5y = −13 →
  26. 26.x + 4y = −22 and 6x + 5y = −37 →
  27. 27.4x + 5y = −23 and 3x − y = −22 →
  28. 28.6x − 4y = −60 and 2x + 2y = 10 →
  29. 29.4x − 6y = 20 and 5x + 2y = 44 →
  30. 30.4x + 9y = −53 and 9x + 4y = 27 →
  31. 31.5x − 2y = 19 and 5x + 5y = 40 →
  32. 32.3x − 5y = 56 and 3x + 2y = 7 →
  33. 33.9x + 5y = 86 and 5x + 9y = 54 →
  34. 34.2x + 5y = 36 and 6x + 5y = 48 →
  35. 35.6x + 2y = 0 and 5x + 4y = 14 →
  36. 36.5x + 9y = 9 and 9x + 5y = 61 →
  37. 37.5x + y = −13 and 5x + 4y = −37 →
  38. 38.x + 3y = 18 and 4x − 2y = 16 →
  39. 39.4x − 3y = −18 and x − 3y = 0 →
  40. 40.3x − 4y = 39 and 4x + 2y = 8 →

Answer key

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

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