Final answer:
To find x and y using matrices from the given equations, we re-write them in standard form and represent them as a matrix equation. The solution involves finding the inverse of the coefficient matrix and multiplying it by the constants matrix.
Step-by-step explanation:
The given system of equations is -8 - 13y = -7x and 7 - 14x = 5 - y. To solve for x and y using matrices, these equations need to be expressed in standard form (Ax + By = C). The standard form of the equations is 7x + 13y = -8 and 14x + y = 2. We can write this system as a matrix equation, Ax = B, where A is the coefficient matrix, x is the column matrix of variables, and B is the column matrix of constants.
To find x and y, we calculate the inverse of matrix A (if it exists) and multiply it by matrix B. This process involves finding the determinant of matrix A, adjugate of A, and finally multiplying the adjugate by 1/det(A) to find A-1. The matrix B remains as is, and after multiplying A-1 by B, we get the values of x and y.