math

Use a matrix equation to solve the system of equations.

6x + 2y = 11
3x - 8y =1
My textbook gave this example, but explained it in a really weird way and I don't understand how to do it. Can someone help?

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  1. What method was used?
    Did they show the inverse matrix?
    Did they use something called row-reduced echelon form?

    (I would never think of using matrices for a system this simple)

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  2. 6x + 2y = 11
    3x - 8y =1
    The matrix equation is
    AX=B
    where A =
    (6 2)
    (3 -8)
    X =
    (x)
    (y)
    and B =
    (11)
    (1)
    Since AX=B, if you multiply on the left by A^-1, you get
    A^-1 * A X = A^-1 B
    So, find A^-1, multiply by B and you end up with a 2x1 matrix which is the solution. See here:

    www.wolframalpha.com/input/?i=%7B%7B6,2%7D,%7B3,-8%7D%7D*%7B%7Bx%7D,%7By%7D%7D+%3D+%7B%7B11%7D,%7B1%7D%7D

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  3. btw, Wolfram also let's you find the inverse matrix

    https://www.wolframalpha.com/input/?i=inverse+%7B%7B6,2%7D,%7B3,-8%7D%7D

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  4. I understand how to find the determinant, but my textbook also showed a part about how to get the solution for x and y, which I didn't understand. It said to multiply each side of the matrix equation by the inverse matrix, although I didn't understand what that meant and couldn't figure out how they did it. It says that the solution is (5/3, 1/2)

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  5. If they expect you to solve this using an inverse matrix, they must have shown
    you how to find that matrix.
    The last link I gave you from Wolfram showed what that matrix is.

    There is a quick way to find the inverse of a 2 by 2
    start with
    a b
    c d
    find the determinant D, you said you knew how: D = (ad - bc)

    inverse is
    d/D -b/D
    -c/D a/D
    or
    (1/D) times

    d -b
    -c a
    in your case that becomes in reduced form

    4/27 1/27
    1/18 -1/9

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