# Solve [[-6,3],[3,5]][[x,-2],[y,-6]]=[[27,-6],[-7,-36]]

Find the inverse matrix of .
The inverse of a matrix can be found using the formula where is the determinant of .
If then
The determinant of is .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Subtract from .
Substitute the known values into the formula for the inverse of a matrix.
Simplify each element of the matrix .
Rearrange .
Rearrange .
Multiply by each element of the matrix.
Simplify each element of the matrix .
Rearrange .
Rearrange .
Rearrange .
Rearrange .
Assuming that is the matrix to solve for, multiply the inverse matrix by both sides of the equation .
Simplify the left side of the equation.
Multiply each row in the first matrix by each column in the second matrix .
Simplify each element of the matrix by multiplying out all the expressions.
Multiplying the identity matrix by any matrix is matrix .
Simplify the right side of the equation.
Multiply each row in the first matrix by each column in the second matrix .
Simplify each element of the matrix by multiplying out all the expressions.
is in the most simplified form.
Solving for the variables in , the answer is .
Solving for the variables in , the answer is .
Solve [[-6,3],[3,5]][[x,-2],[y,-6]]=[[27,-6],[-7,-36]]

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