Write the augmented matrix of the following system of equations.
\[
\left\{\begin{array}{r}
-2 x+y-3=0 \\
x-5 y+6=0
\end{array}\right.
\]
What is the augmented matrix?

Step 1 ：The given system of equations is: \[\begin{align*} -2x + y - 3 &= 0 \\ x - 5y + 6 &= 0 \end{align*}\]

Step 2 ：The augmented matrix is a way to represent a system of equations in a compact form. It is formed by writing the coefficients of the variables and the constants from the right-hand side of the equations as the entries of a matrix. The coefficients of each variable form a column in the matrix, and each equation forms a row.

Step 3 ：For the given system of equations, the coefficients of x in the first and second equations are -2 and 1 respectively. The coefficients of y are 1 and -5. The constants on the right-hand side of the equations are -3 and 6.

Step 4 ：So, the augmented matrix for the given system of equations is: \[\begin{bmatrix} -2 & 1 & |-3| \\ 1 & -5 & |6| \end{bmatrix}\]

Step 5 ：Final Answer: The augmented matrix for the given system of equations is \[\boxed{\begin{bmatrix} -2 & 1 & |-3| \\ 1 & -5 & |6| \end{bmatrix}}\]