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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 807 · 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. 1.2x + 4y = 42 and 3x + 4y = 49 →
  2. 2.9x + 2y = 51 and 2x + 9y = 37 →
  3. 3.4x + 2y = 4 and 4x + 5y = 16 →
  4. 4.3x + 5y = −16 and 5x − 3y = −38 →
  5. 5.6x + 5y = −13 and 5x − 4y = −68 →
  6. 6.2x + 6y = 46 and 4x − 2y = 22 →
  7. 7.3x + 4y = 36 and x + 3y = 17 →
  8. 8.x + 6y = 16 and 4x + 4y = −16 →
  9. 9.2x − 5y = −13 and 2x + 5y = 17 →
  10. 10.x − 5y = −26 and 6x + y = −32 →
  11. 11.4x − y = −13 and 4x − 3y = −23 →
  12. 12.4x − 4y = 24 and 3x − 4y = 17 →
  13. 13.3x + 6y = 36 and 6x + 3y = 54 →
  14. 14.3x + 6y = 39 and 5x + 5y = 35 →
  15. 15.x + 9y = −58 and 9x + y = 38 →
  16. 16.2x + 5y = 29 and x − 3y = −13 →
  17. 17.2x − 2y = 8 and 2x + 3y = 18 →
  18. 18.2x + 6y = 22 and 6x + 2y = 50 →
  19. 19.9x + 2y = 93 and 2x + 9y = 72 →
  20. 20.4x − 4y = −4 and 6x + 3y = 21 →
  21. 21.5x + 5y = 40 and x + 3y = 22 →
  22. 22.4x − 6y = 16 and 4x − 4y = 12 →
  23. 23.3x + 8y = 37 and 8x + 3y = 7 →
  24. 24.3x + y = 20 and 5x + 6y = 68 →
  25. 25.x + 8y = 20 and 8x + y = −29 →
  26. 26.x + 5y = 46 and 6x − 3y = −21 →
  27. 27.9x + 3y = 69 and 3x + 9y = 39 →
  28. 28.2x + y = 18 and 5x + y = 33 →
  29. 29.2x + 6y = 2 and 2x + 3y = −4 →
  30. 30.2x − 5y = 20 and 5x − 6y = 11 →
  31. 31.6x − 4y = −4 and 4x + 5y = −41 →
  32. 32.3x − y = 14 and 6x − 4y = 44 →
  33. 33.3x − 3y = 6 and 3x + 2y = −9 →
  34. 34.4x + 6y = 46 and 5x + 4y = 47 →
  35. 35.5x + 3y = 14 and 6x − 6y = −12 →
  36. 36.x + 4y = −14 and 4x + y = 19 →
  37. 37.6x + 5y = −59 and 3x − 4y = 16 →
  38. 38.x − 2y = −22 and 6x − 2y = −52 →
  39. 39.7x + y = 52 and x + 7y = −20 →
  40. 40.x + y = 3 and 4x + 5y = 13 →

Answer key

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

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