Write a system of linear equations for the problem and solve the system using an augmented matrix and your calculator.

Mike works a total of $60 \mathrm{hr}$ per week at his two jobs. He makes $\$ 6$ per hour at job A and \$7 per hour at job B. If his total pay for one week is $\$ 381$ before taxes, then how many hours does he work at each job?

He works $\square$ hr at job A and $\square$ hr at job B.

Step 1 ：Let's denote the number of hours Mike works at job A as \(x\) and the number of hours he works at job B as \(y\).

Step 2 ：From the problem, we have two equations: \(x + y = 60\) and \(6x + 7y = 381\).

Step 3 ：We can write this system of equations as an augmented matrix: \[\begin{bmatrix} 1 & 1 & 60 \\ 6 & 7 & 381 \end{bmatrix}\]

Step 4 ：To solve this system, we can use the method of elimination. First, we will multiply the first row by 6 and the second row by 1 to make the coefficients of \(x\) in the two equations the same: \[\begin{bmatrix} 6 & 6 & 360 \\ 6 & 7 & 381 \end{bmatrix}\]

Step 5 ：Then, we subtract the first row from the second row: \[\begin{bmatrix} 6 & 6 & 360 \\ 0 & 1 & 21 \end{bmatrix}\]

Step 6 ：This gives us \(y = 21\).

Step 7 ：Substitute \(y = 21\) into the first equation of the original system, we get: \(x + 21 = 60\)

Step 8 ：Solving for \(x\), we get \(x = 60 - 21\)

Step 9 ：So, \(x = 39\)

Step 10 ：Therefore, Mike works \(\boxed{39}\) hours at job A and \(\boxed{21}\) hours at job B.