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

Step 1 ：The given system of equations is: $$\begin{array}{rl}-2x+y-3& =0\\ x-5y+6& =0\end{array}$$

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: $$\left[\begin{array}{ccc}-2& 1& |-3|\\ 1& -5& |6|\end{array}\right]$$

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