are all linear equations able to be solved by matrices or matrix method.

Question

I used substitution method and got one answer then used matrix method and got a completely different answer

Answer 1

If a solution exists and if there are as many independent linear equations as unknowns, you should be able to solve the problem either way.  If you are getting different answers, there has to be a math error somewhere.  How big is your matrix?  I have spreadsheets set up to solve systems with 2x2 and 3x3 matrices, and I can quickly test you answers.  If your matrix is no bigger than 3x3, enter the rows in the Comment window and I can check it.

Answer 2

You actually have two questions. First, the choice of method should not create different answers. This indicates you made a mistake somewhere. Matrices are great for creating errors, so I wouldn't be surprised if it was responsible.

Secondly, you asked if every linear system can be solved by a matrix. No. Some systems have no solutions. If true, you would find substitution produces a contradiction, such as " 0 = 17". Likewise, the matrices would produce an error as well.