Read the result
Follow the pivots down the diagonal. Each row operation removes one coefficient below a pivot and pushes the system toward triangular form.
Linear systems
Gaussian Elimination Solver
Solve a 3x3 system by row reduction, with each elimination step kept in view.
Formula
[A|b] -> [U|y], then x_i = (y_i - sum u_ij*x_j)/u_ii
Result
Worked substitution
The row operations are chosen to remove entries below each pivot while preserving the solution.
Where it helps
Use it when three equations are too awkward for substitution but still small enough to inspect by hand.
Common slip
Do not judge the answer only by the final numbers. Check the residual against the original equations.
Try it
Set a first-column entry below the pivot to 0 and notice that the corresponding elimination step disappears.