List your equations in a vertical row. Make sure all of your variables appear in the same order in the equations so that each type of variable will line up vertically. For example, if you have three 3-variable equations (variables x,y and z), you line your equations up so that the Xs are all in a column, the Ys are all in a colum and the Zs are all in a column.
Draw an empty set of brackets to the right of your list of equations. If you have three 3-variable equations, make the brackets large enough to contain 3 rows and 4 columns.
Fill in the bracket with the coefficients of the equations. If your first equation reads "3X + Y - 4Z = 9," the first row of your bracket will read [3 1 -4 9]. Repeat with the remaining equations, ensuring that the X coefficients are all in the first column, the Y coefficients line up in the second column and so on.
Perform elementary row operations to reduce your matrix to row-echelon form. Remember that elementary row operations allow you to (a) multiply a row by a nonzero constant, (b) add one row to another row and (c) multiply a row by a nonzero constant and add it to another row.
Read the solutions. The "1" in the column that contained the X coefficients will line up horizontally with the solution to X; the '1" in the column that contained the Y coefficients will line up with the solution to Y and so on.
Write down your solutions in the form of X=, Y= and Z=. Circle your answer. You have found the solution.