Systems of Linear Equations: Three Variables · Try It 1

Solve the system of linear equations with three variables.
\left\{\begin{matrix} x + 2 y - 3 z = - 1 \\ x - 3 y + z = 1 \\ 2 x - y - 2 z = 2 \end{matrix}\right \begin{matrix}\left(1\right) \\ \left(2\right) \\ \left(3\right)\end{matrix}

\begin{array}{|c|c|}\hline \text{Step 1} & \text{Write the equations in standard form. If any coefficients are fractions, clear them. ________________________________________} \\ \hline \text{Step 2} & \text{Let's use equations (1) and (2) to eliminate }x\text{ ________________________________________} \\ \hline \text{Step 3} & \text{Let's use equations (1) and (3) to eliminate }x\text{ ________________________________________} \\ \hline \text{Step 4} & \text{Let's now use the new equations (4) and (5) to eliminate }y\text{ ________________________________________} \\ \hline \text{Step 5} & \\ \hline \text{Step 6} & \\ \hline\end{array}

This exercise has fill-in blanks from its source book and no answer key.

OpenStax, Algebra and Trigonometry 2e · §11.2 Systems of Linear Equations: Three Variables · Try It 1