In Example 1, change the 18 to 19 and then solve the system of equations.

Data from Example 1

Use matrices to solve the system of equations

The matrices for Eq. (16.7), and the matrix equation are

By either of the methods of the previous section, we can determine the inverse of matrix A to be

We now form the matrix product A⁻¹C.

Because X = A⁻¹C, this means that

Therefore, the required solution is x = 3 and y = −1, which checks when these values are substituted into the original equations. See the calculator matrix solution shown in Fig. 16.11.

2x - y = 7 5x - 3y = 18