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anonymous

  • 4 years ago

Use Cramer's rule to solve the system of equations. { 2x+3y=4 x-2y=9

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  1. anonymous
    • 4 years ago
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    Are you studying matrices / linear algebra?

  2. anonymous
    • 4 years ago
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    yes!

  3. anonymous
    • 4 years ago
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    Great, so how far have you got until now?

  4. anonymous
    • 4 years ago
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    (If you're stuck from the beginning, that's fine too though!)

  5. anonymous
    • 4 years ago
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    i understand how to do it, just the last step is where i mess up. I only know how to put them into the matrix sets, and solve those out. but i have no idea where to go from there.

  6. anonymous
    • 4 years ago
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    As I remember it, you create a square matrix A (left hand side of the equation) and column (that's vertical) vector b (right side of the equation). To get x, you replace the first column of your square matrix with vector b, whereas for y you replace the second column of your square matrix with vector b instead. In both cases, you then take the determinant of the new matrix you've created, and divide by the determinant of the original square matrix A. Does that make sense?

  7. anonymous
    • 4 years ago
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    If so, we can try it with the numbers now?

  8. anonymous
    • 4 years ago
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    If that doesn't make sense, we can do it using Draw.

  9. anonymous
    • 4 years ago
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    \[\left[\begin{matrix}2 & 3 \\ 1 & -2\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}4 \\ 9\end{matrix}\right)\]

  10. anonymous
    • 4 years ago
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    yea i understand,

  11. anonymous
    • 4 years ago
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    Thanks iven5880!

  12. anonymous
    • 4 years ago
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    I'm still working on it. I'm not goot at using this editor

  13. anonymous
    • 4 years ago
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    So the original square matrix is the one that iven5880 has laid out, and whose determinant is 2*-2 -3*1 = -4-3=-7.

  14. anonymous
    • 4 years ago
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    |dw:1327953451141:dw|

  15. anonymous
    • 4 years ago
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    Awesome!

  16. anonymous
    • 4 years ago
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    arricuhh, does that part make sense to you?

  17. anonymous
    • 4 years ago
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    *airricuhh

  18. anonymous
    • 4 years ago
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    So x = -35/-7 = 5

  19. anonymous
    • 4 years ago
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    yea, i understand (:

  20. anonymous
    • 4 years ago
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    Can you do the same thing for y?

  21. anonymous
    • 4 years ago
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    can you help me with me it /:

  22. anonymous
    • 4 years ago
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    OK, how are you going to start?

  23. anonymous
    • 4 years ago
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    |dw:1327953694308:dw|

  24. anonymous
    • 4 years ago
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    So y = 14/-7 = 2

  25. anonymous
    • 4 years ago
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    oh, welll.. thank you iven5880! and thank you BasketWeave

  26. anonymous
    • 4 years ago
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    You're welcome! Mostly thanks to iven5880 though, I'd say :D

  27. anonymous
    • 4 years ago
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    :))

  28. anonymous
    • 4 years ago
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    You're welcome and thanks BasketWeave

  29. anonymous
    • 4 years ago
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    :)

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