Answer:
[tex]x=-3,y=6,z=-3[/tex].
Step-by-step explanation:
We have been given a system. We are asked to solve our given system of equations.
[tex]x+y+z=0...(1)[/tex]
[tex]2x+4y+2z=12...(2)[/tex]
[tex]-x+9y-3z=66...(3)[/tex]
From equation (1), we will get:
[tex]x=-y-z...(1)[/tex]
Upon substituting this value in equation (2), we will get:
[tex]2(-y-z)+4y+2z=12\\\\ -2y-2z+4y+2z=12\\\\2y=12\\\\y=\frac{12}{2}\\\\y=6[/tex]
Upon substituting [tex]x=-y-z[/tex] in equation (3), we will get:
[tex]-(-y-z)+9y-3z=66\\\\y+z+9y-3z=66\\\\10y-2z=66\\\\10(6)-2z=66\\\\-2z=66-60\\\\-2z=6\\\\ \frac{-2z}{-2}=\frac{6}{-2}\\\\z=-3[/tex]
Let us solve for x as:
[tex]x=-y-z\\\\ x=-6-(-3)\\\\x=-6+3\\\\x=-3[/tex]
Therefore, the solutions of our given system is [tex]x=-3,y=6,z=-3[/tex].
