What type of question can be solved using Cramer's rule?
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When using Cramer's rule, you will take the determinant.  To find the determinant, we convert the system of equations into a matrix.

When forming the matrix, you will have a column of coefficients that correspond to the variables.  The lowest variable is the first column.  So here is our matrix.  Call this matrix M.

3         -2           5

9         -8           1

-6        -4           7

Then find the determinant of this matrix.  That is det(M).

Next, you will find the determinant for each column.

Find det(x) using the matrix

6        -2         5

46      -8         1

27      -4         7

Then find det(y) using the matrix

3        6         5

9        46       1

-6       27       7

Then find det(z) using the matrix

3         -2           6

9         -8           46

-6        -4           27

Notice that in the last three matrices, the coefficients on the right side of the equation correspond to the columns of the specific determinants.

So now your solutions are

x = det(x) / det(M)

y = det(y) / det(M)

z = det(z) / det(M)

Step-by-step explanation:

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