Writing a System of Equations from an Augmented Matrix Form

Find the system of equations from the augmented matrix.

[\begin{array}{r} 1 & −3 & −5 \\ 2 & −5 & −4 \\ −3 & 5 & 4 \end{array} | \begin{array}{r} −2 \\ 5 \\ 6 \end{array}]

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
When the columns represent the variables $x,$ $y,$ and $z,$

$[\begin{array}{r} 1 & −3 & −5 \\ 2 & −5 & −4 \\ −3 & 5 & 4 \end{array} | \begin{array}{r} −2 \\ 5 \\ 6 \end{array}] \to \begin{array}{l} x - 3 y - 5 z = - 2 \\ 2 x - 5 y - 4 z = 5 \\ −3 x + 5 y + 4 z = 6 \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the system of equations from the augmented matrix.

[\begin{matrix} 1 & −1 & 1 \\ 2 & −1 & 3 \\ 0 & 1 & 1 \end{matrix} | \begin{matrix} 5 \\ 1 \\ −9 \end{matrix}]

How did it go?