91Ó°ÊÓ

We are given system of linear equations$\left\{\begin{array}{l}x-3y+z=-5\\ -3x-y-z=1\\ 2x-2y+3z=1\end{array}\right.$and coordinate $(2,-2,3)$.

Substituting $$\begin{gathered} x=2 \\ y=-2 \\ z=3 \end{gathered}$$in given equation and checking whether the equations is true or not.

Checking first equation $x-3y+z=-5$,

$$\begin{gathered} 2-3(-2)+3=-5 \\ 2+6+3=-5 \\ 11≠-5 \end{gathered}$$

Hence $(2,-2,3)$is not the solution of given system of linear equation.

We are given system of linear equations$\left\{\begin{array}{l}x-3y+z=-5\\ -3x-y-z=1\\ 2x-2y+3z=1\end{array}\right.$and coordinate $(-2,2,3)$.

Substituting $$\begin{gathered} x=-2 \\ y=2 \\ z=3 \end{gathered}$$in given equation and checking whether the equations is true or not.

Checking first equation $x-3y+z=-5$,

$$\begin{gathered} -2-3\left(2\right)+3=-5 \\ -2-6+3=-5 \\ -5=-5 \end{gathered}$$

This is True.

Checking second equation $-3x-y-z=1$,

$$\begin{gathered} -3(-2)-2-3=1 \\ 6-2-3=1 \\ 1=1 \end{gathered}$$

This is also true.

Checking third equation $2x-2y+3z=1$,

$$\begin{gathered} 2(-2)-2\left(2\right)+3\left(3\right)=1 \\ -4-4+9=1 \\ 1=1 \end{gathered}$$

This is also true.

Hence$(-2,2,3)$is solution of given system of linear equations.