Find values for the variables so that the following matrices are equal. \[ \left[\begin{array}{rr} x & 5 y \\ z & 6 \end{array}\right]=\left[\begin{array}{rr} 12 & 15 \\ 7 & 6 \end{array}\right] \] $x=\square($ Simplify your answer.) $y=\square($ Simplify your answer.) $z=\square$ (Simplify your answer.)

Step 1 ：Given the matrices \(\left[\begin{array}{rr} x & 5 y \ z & 6 \end{array}\right]\) and \(\left[\begin{array}{rr} 12 & 15 \ 7 & 6 \end{array}\right]\), we need to find the values of \(x\), \(y\), and \(z\) that make these matrices equal.

Step 2 ：For two matrices to be equal, their corresponding elements must be equal. This gives us the system of equations: \(x = 12\), \(5y = 15\), and \(z = 7\).

Step 3 ：Solving the first equation gives \(x = 12\).

Step 4 ：Solving the second equation gives \(y = 3\).

Step 5 ：Solving the third equation gives \(z = 7\).

Step 6 ：Final Answer: The solution to the system of equations is \(x=\boxed{12}\), \(y=\boxed{3}\), and \(z=\boxed{7}\).