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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 85 · 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 − 2y = 30 and 6x + y = 15 →
  2. 2.5x + 8y = 96 and 8x + 5y = 99 →
  3. 3.6x + 9y = 33 and 9x + 6y = 27 →
  4. 4.9x + 2y = 52 and 2x + 9y = 80 →
  5. 5.x − 6y = 44 and x − 5y = 38 →
  6. 6.x + y = 4 and 3x + 2y = 5 →
  7. 7.x + y = 16 and 6x + 3y = 75 →
  8. 8.5x + 7y = −39 and 7x + 5y = −21 →
  9. 9.x + 4y = −12 and 6x − 3y = −18 →
  10. 10.2x + 4y = 6 and 4x + 2y = 18 →
  11. 11.5x + y = 27 and x + 5y = −9 →
  12. 12.3x − y = 5 and 4x − 2y = 6 →
  13. 13.2x − y = −22 and 5x + y = −41 →
  14. 14.6x − 4y = 40 and x + 2y = −12 →
  15. 15.4x + 6y = −8 and 3x + 3y = 0 →
  16. 16.2x + 5y = 8 and 5x + 2y = 41 →
  17. 17.3x − 4y = 52 and 5x + 6y = −2 →
  18. 18.2x − 3y = 16 and 2x − 6y = 28 →
  19. 19.5x + 5y = −85 and 2x + y = −25 →
  20. 20.4x − 3y = −16 and 2x − 3y = −2 →
  21. 21.4x + 3y = 17 and 3x + 4y = 11 →
  22. 22.4x − 5y = −14 and 5x − 6y = −16 →
  23. 23.4x + 3y = 7 and x + y = 2 →
  24. 24.4x − 5y = −6 and 4x + 6y = 16 →
  25. 25.4x − 5y = −34 and x + 6y = 35 →
  26. 26.4x + 4y = 40 and 4x + y = 16 →
  27. 27.x + 9y = 74 and 9x + y = −54 →
  28. 28.4x + y = 13 and 5x + 4y = 41 →
  29. 29.7x + 2y = 10 and 2x + 7y = −55 →
  30. 30.4x − y = 28 and 2x + 4y = 32 →
  31. 31.5x + 2y = 14 and 4x + 3y = 0 →
  32. 32.x + 2y = 5 and 2x − 3y = −18 →
  33. 33.6x − 5y = 43 and x + 5y = −22 →
  34. 34.3x − 3y = −21 and x + 2y = −13 →
  35. 35.3x + 5y = −22 and 5x + 3y = 6 →
  36. 36.2x + 5y = 6 and 5x + 2y = 36 →
  37. 37.x + 3y = 13 and 2x + y = 6 →
  38. 38.9x + 6y = −117 and 6x + 9y = −123 →
  39. 39.x + 5y = −42 and 5x + y = −42 →
  40. 40.2x + 5y = 29 and 2x + 6y = 32 →

Answer key

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

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