Consider the following system. $$ \left\{\begin{array}{l} -x+2 y-3 z=1 \ x-y-z=2 \ -3 x+4 y-z=-3 \end{array}\right. $$ Choose the best description of its solution. If applicable, give its solution. The system has no solution. The system has a unique solution. $$ (x, y, z)=(\square . \square \square) $$ The system has infinitely many solutions. $$ (x, y, z)= $$ $$ (x, \square, \square) $$ (П. $$ y, \square) $$ (ㄴ. $$ 1 . z) $$

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Solve the system of equations $$ -x+2y-3z=1;x-y-z=2;-3x+4y-z=-3 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}-x+2y-3z=1\x-y-z=2\-3x+4y-z=-3\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=-1+2y-3z\x-y-z=2\-3x+4y-z=-3\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\left\{ \begin{array}{l}-1+2y-3z-y-z=2\-3\left(-1+2y-3zight)+4y-z=-3\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}-1+y-4z=2\3-2y+8z=-3\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}y=3+4z\3-2y+8z=-3\end{array}ight.$$
- step5: Substitute the value of $$y:$$
  $$3-2\left(3+4zight)+8z=-3$$
- step6: Simplify:
  $$-3=-3$$
- step7: Substitute the value of $$y:$$
  $$x=-1+2\left(3+4zight)-3z$$
- step8: Simplify:
  $$x=5+5z$$
- step9: Calculate:
  $$\left(x,y,zight) = \left(5+5z,3+4z,zight),z \in \mathbb{R}$$
- step10: Alternative Form:
  $$	extrm{Infinitely many solutions}$$
The system of equations has infinitely many solutions. Therefore, the best description of its solution is that it has infinitely many solutions.

Since the system has infinitely many solutions, we cannot provide a specific solution in the form of $$(x, y, z)$$. The solution will be in the form of $$(x, y, z) = (x, y, z)$$ where $$x$$, $$y$$, and $$z$$ can take any values that satisfy the system of equations.
The system has infinitely many solutions.

Consider the following system.

Choose the best description of its solution. If applicable, give its solution.
The system has no solution.
The system has a unique solution.

The system has infinitely many solutions.

(П.
(ㄴ.

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Consider the following system. Choose the best description of its solution. If applicable, give its solution. The system has no solution. The system has a unique solution. The system has infinitely many solutions. (П. (ㄴ.