The linear system

$$\begin{array}{rcrcrcr} & & & - & 2 x_{3} & = & -4 \\ & - & x_{2} & - & x_{3} & = & -14 \\6 x_1 & + & 6 x_{2} & + & 6 x_{3} & = & 0\end{array}$$

is not in echelon form.

Begin by choosing which of the following statements are correct. If there is more than one reason why the system is not in echelon form, type the letters as a comma separated list.

A. The system is not in echelon form because a variable is the leading variable of two or more equations.
B. The system is not in echelon form because the system is not organized in a descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.
C. The system is not in echelon form because not every equation has a leading variable.

Correct Letter(s):

Now write the system in echelon form.

Equation 1:
Equation 2:
Equation 3:

Finally, solve the system. Use x1, x2, and x3 to enter the variables $x_1$, $x_2$, and $x_3$. If necessary, use s1, s2, etc. to enter the free variables $s_1$, $s_2$, etc.

$(x_1, x_2, x_3) = \bigg($ , , $\bigg)$