Use Gaussian reduction to solve the system $$\begin{aligned} x-2y+z \amp= -1\qquad\qquad \amp\amp (1)\\ \frac{2}{3}x +\frac{1}{3}y - z \amp= -1 \amp\amp (2)\\ 3+3y-2z \amp= 10 \amp\amp (3) \end{aligned}$$ Follow the steps:

• Step 1: Clear the fractions from Equation (2).
• Step 2: Eliminate $z$ from Equations (1) and (2).
• Step 3: Eliminate $z$ from Equations (1) and (3).
• Step 4: Eliminate $x$ from your new $2\times 2$ system.
• Step 5: Form a triangular system and solve by back-substitution.

Give the solution as an ordered triple.