Answer: The system of equations has no solutions.
Step-by-step explanation:
Identify the equation as:
[tex]x + 2y - z=3[/tex] [Equation 1]
[tex]2x -y + 2z=6[/tex] [Equation 2]
[tex]x - 3y + 3z=4[/tex] [Equation 3]
Multiply [Equation 1] by -2 and add this to [Equation 2] :
[tex](-2)(x + 2y - z)=3(-2)[/tex]
[tex]\left \{ {{-2x - 4y +2z=-6} \atop {2x -y + 2z=6}} \right.\\ ..........................\\-5y+4z=0[/tex]
Find another equation of two variables: Multiply [Equation 3] by -2 and add this to [Equation 2]:
[tex](-2)(x - 3y + 3z)=4(-2)[/tex]
[tex]\left \{ {{2x -y + 2z=6} \atop {-2x +6y -6z=-8}} \right.\\........................\\5y-4z=-2[/tex]
Then you get this new system of equations. When you add them, you get:
[tex]\left \{ {{-5y+4z=0} \atop {5y-4z=-2}} \right.\\..................\\0=-2[/tex]
Since the obtained is not possible, the system of equations has no solutions.
