multiply 2x - y + z = - 2 for 3
[tex]6x-3y+3z=-6[/tex]then sunstract the equation 1 and 2
[tex]\begin{gathered} 6x+3y-4z=8 \\ 6x-3y+3z=-6 \\ 6y-7z=14 \end{gathered}[/tex]multiply -3x+2y+3z=-6 for 2
[tex]-6x+4y+6z=-12[/tex]adding
[tex]\begin{gathered} -6x+4y+6z=-12 \\ \underline{6x-3y+3z=-6} \\ y+9z=-18 \end{gathered}[/tex]multiply y+9z=-18 for 6
[tex]6y+54z=-108[/tex]Subtracting
[tex]\begin{gathered} 6y+54z=-108 \\ \underline{6y-7z=14} \\ 61z=-122 \end{gathered}[/tex]then solve
[tex]\begin{gathered} 61z=-122 \\ \frac{61z}{61}=\frac{-122}{61} \\ z=-2 \end{gathered}[/tex][tex]\begin{gathered} 6y-7\mleft(-2\mright)=14 \\ 6y+14=14 \\ 6y+14-14=14-14 \\ 6y=0 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} 6x-3\cdot\: 0+3\mleft(-2\mright)=-6 \\ 6x-6=-6 \\ 6x-6+6=-6+6 \\ 6x=0 \\ x=0 \end{gathered}[/tex]answer is: x = 0, y = 0 and z = - 2
