$$ 9 _ { 3 . } | \left. \begin{array} { l }{ x + y + 2 z = 2 } \ { + 2 y - z = 2 } \ { x + 3 y + z = 0 } \end{array} ight. $$

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$$ 9 _ { 3 . } | \left. \begin{array} { l }{ x + y + 2 z = 2 } \ { + 2 y - z = 2 } \ { x + 3 y + z = 0 } \end{array} ight. $$

UpStudy AI · Accepted Answer

Натиснете "Решете системата от уравнения" за да получите решението.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x+y+2z=2\2y-z=2\x+3y+z=0\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=2-y-2z\2y-z=2\x+3y+z=0\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$\left\{ \begin{array}{l}2y-z=2\2-y-2z+3y+z=0\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}2y-z=2\2+2y-z=0\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}z=-2+2y\2+2y-z=0\end{array}ight.$$
- step5: Substitute the value of $$z:$$
  $$2+2y-\left(-2+2yight)=0$$
- step6: Simplify:
  $$4=0$$
- step7: Calculate:
  $$\left\{ \begin{array}{l}x \in \varnothing \y \in \varnothing \z \in \varnothing \end{array}ight.$$
- step8: Rewrite:
  $$(x, y, z) \in \varnothing$$
Системата от уравнения не има решение.
Системата от уравнения не има решение.

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