I already know the 3 methods of doing it, but I recently found out about using matrices to solve it.

How exactly do you do that? All I can remember is something with rref on my calculator.

http://en.wikipedia.org/wiki/Gaussian_elimination

Thanks, but that doesn't tell me about the rref thingy that I saw my teacher do.

I don't know about rref. You can use a calculator to compute the inverse of a matrix, do Gaussian elimination, or use Cramer's rule which uses determinants of matrices...

I googled rref and it says "reduced row echelon form"

http://math.la.asu.edu/~kolossa/119/calc.html

Thanks alot! This is going to help me solve these system of linear equations so much faster.

Using matrices to solve a system of linear equations allows you to perform computations more efficiently and systematically. The Reduced Row Echelon Form (rref) technique is a common method used to solve systems of equations using matrices. Here's a step-by-step guide on how to use matrices and rref to solve a system of linear equations:

Step 1: Set up the augmented matrix:
- Write the coefficients of each variable and the constants on the left-hand side of the equations as a matrix, separating the coefficients and constants with a vertical bar. Each row in the matrix represents an equation, and each column corresponds to a variable, with the last column representing the constants.

Step 2: Perform row operations on the augmented matrix:
- Use row operations to reduce the matrix to its Reduced Row Echelon Form (rref). The goal is to transform the matrix into a triangular form, where the leading coefficient of each row is 1 and all elements below the leading coefficient are zeros.

Step 3: Solve for the variables:
- Read and interpret the rref matrix to determine the solutions to the system of equations. Each row represents an equation, and the value in the last column corresponds to the constant on the right-hand side of the equation. The leading coefficient (1's) tells you what each variable is equal to.

Step 4: Express the solution in both parametric and explicit form (if necessary):
- If you have infinitely many solutions, express the solution in parametric form using the variables that don't have leading coefficients. If you have unique solutions, express them in explicit form.

To execute these steps, you can either use a graphing calculator or matrix software such as MATLAB or Wolfram Alpha. For a graphing calculator, you would typically enter the augmented matrix and then use the rref function to find the reduced row echelon form.