How can matrices be used when solving by substitution?
The process of "solving" a matrix and solving a system of equations are mathematically identical.
Suppose you have some system with
This is equivalent to the matrix equation
To solve this, one would set up an augmented matrix and use row-reduction techniques to find your solution. The bolded methods are outside the scope of basic algebra and you will run across them if you ever take a linear algebra course.
Just know that row-reduction techniques simulate substitution and that it is not (mathematically) easier to use a matrix to solve a system than to solve a system in the traditional way.