 Recall that when you wanted to solve a system of equations, you used to use two different methods.  Substitution Method  Addition Method

 When using matrices to solve a system of equations, you go through the same process you would when applying the addition method.  The only difference is that with a matrix you do not write the variables.

Solve the following system of equations using the addition method.

Multiply one equation by a non- zero constant Add the equations together, eliminating one variable and solve for the other Solution

Substitute this value into one equation and solve for the other variable. Substitute y = 4 and solve for x

 When performing row operations we go through this exact process.

 When performing row operations, you can interchange one row with another.  This is the same as changing the place of two equations when adding them.

 You can multiply the elements of a matrix by a non-zero number.  This is the same as multiplying both sides of an equation by a non-zero number.

 After multiplying any row by a non-zero number, you can add this row to another row in the matrix.  This is the same as adding equations together in order to eliminate a variable.

 When you multiply one row by a non-zero number and add the values to another row, the values in the row you began with do not change.  The values in the other row change.

 There is nothing wrong with writing out the new products in the row you are multiplying.  If it helps you keep track of your work then go for it, just remember to simplify at the end.