Gaussian Elimination and Gauss-Jordan Elimination Three-Variable Linear System

In this lesson, we will learn about Gaussian Elimination and Gauss-Jordan Elimination with three variables. These methods allow us to quickly solve a linear system using a matrix versus traditional methods that were employed in Algebra 1 and Algebra 2. First, we will set up each equation of our system in standard form: ax + by + cz = d, where a, b, c, and d are real numbers. Then we will write the numerical information (the coefficients and constants) in an augmented matrix. Once in this form, we will perform row operations in order to transform the matrix into row-echelon form (Gaussian Elimination) or reduced-row echelon form (Gauss-Jordan Elimination).

[constantinospsaras]

how is y=6? I'm finding x=0, y=3 and z=-5