# Solve Using an Inverse Matrix 4x+2=5y-3 , y=3x-1

,

Find the from the system of equations.

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 .

Left multiply both sides of the matrix equation by the inverse matrix .

Any matrix multiplied by its inverse is equal to all the time. . .

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.

The equation after simplifying the right and left side of the equation is .

Find the solution.

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