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Math Help - Cramer's rule setup question

  1. #1
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    Cramer's rule setup question

    I am not sure how to solve this problem as the setup is different from other problems of this kind I have faced.All I need to know is how to set it up.If you notice the variable x is isolated on the left, usually the constant is in this position and I am not sure how to set this up.

    4x= -5y+10
    5x= -y-19
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  2. #2
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    Hi

    Quote Originally Posted by mr.confused View Post
    I am not sure how to solve this problem as the setup is different from other problems of this kind I have faced.All I need to know is how to set it up.If you notice the variable x is isolated on the left, usually the constant is in this position and I am not sure how to set this up.

    4x= -5y+10
    5x= -y-19
    Not sure about your question, but one possibility is:


    4x= -5y+10
    -> x = (-5y+10)/4

    use this for your second equation 5x= -y-19

    5*[(-5y+10)/4] = -y - 19

    (-25y+50)/4 = -y - 19

    -25y+50 = -4y - 76

    -21y = -126

    => y = (-126)/(-21) = 6

    Now you now y, can you find x?

    You need to solve 4x= -5*(6)+10 OR 5x= -(6)-19

    Remember, (6) is the solution for y. I just wrote 6 instead of y.

    Regards
    Rapha
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  3. #3
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    Although you do have the correct answer for y, My problem is that I think I am supposed to use Cramer's rule to get determinants.It's a strange set up for Cramer's rule, I think.
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  4. #4
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    Okay I figured it out finally:

    Your supposed to to bring -5 and -y over the to the left side so that it looks like this:

    4x+5y=10
    5x+y=-19
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  5. #5
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    Quote Originally Posted by mr.confused View Post
    I am not sure how to solve this problem as the setup is different from other problems of this kind I have faced.All I need to know is how to set it up.If you notice the variable x is isolated on the left, usually the constant is in this position and I am not sure how to set this up.

    4x= -5y+10
    5x= -y-19

    4x+5y=10
    5x+y=-19

    Find the determinant of the coefficient matrix:

    D_c=\begin{vmatrix}4 & 5 \\ 5 & 1 \end{vmatrix}=-21

    Now, find the determinants of the x and y matricies:

    D_x=\begin{vmatrix}10 & 5 \\ -19 & 1 \end{vmatrix}=105

    D_y=\begin{vmatrix}4 & 10 \\ 5 & -19 \end{vmatrix}=-126

    x=\frac{D_x}{D_c}=\frac{105}{-21}=-5

    y=\frac{D_y}{D_c}=\frac{-126}{-21}=6
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