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function augmented_to_upper_triangular_and_solve(A)
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    [rows, cols] = size(A);
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    // Step 1: Convert to upper triangular form using Gaussian elimination
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    for i = 1:min(rows, cols-1) // Only need to process up to the second last column
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        // Make sure the pivot element is non-zero
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        if A(i, i) == 0
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            for j = i+1:rows
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                if A(j, i) != 0
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                    // Swap row i and row j
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                    temp = A(i, :);
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                    A(i, :) = A(j, :);
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                    A(j, :) = temp;
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                    break;
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                end
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            end
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        end
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        // Eliminate entries below the pivot
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        for j = i+1:rows
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            if A(j, i) != 0
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                // Row operation: subtract a multiple of row i from row j
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                factor = A(j, i) / A(i, i);
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                A(j, :) = A(j, :) - factor * A(i, :);
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            end
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        end
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    end
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    // Step 2: Perform back substitution to solve for variables
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    solution = zeros(rows, 1);  // Initialize a vector to store the solution
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    // Start back substitution from the last row
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    for i = rows:-1:1
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        sum = A(i, cols);  // The last column contains the constants (right-hand side of the equations)
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        // Subtract the known values (to the right of the diagonal)
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        for j = i+1:cols-1
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            sum = sum - A(i, j) * solution(j);
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        end
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        // Solve for the current variable
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        solution(i) = sum / A(i, i);
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    end
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    // Step 3: Output the upper triangular matrix and the solution
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    disp("Upper Triangular Matrix:");
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    disp(A);
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    disp("Solution (x, y, z):");
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    disp(solution);
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endfunction