Final answer:
The system of linear equations has infinitely many solutions.
Step-by-step explanation:
The given system of linear equations is:
2 + y + z = 2
2x - 3y + z = 11
-3 + 2y - 2z = -13
We can solve this system by using the method of elimination or substitution. Let's use the method of elimination:
Multiply the first equation by -2 and the second equation by 1:
-4 - 2y - 2z = -4
2x - 3y + z = 11
Adding these two equations, we get:
-2y - z = 7
2x - 3y + z = 11
Now, multiply the third equation by -2 and add it to the second equation:
2x - 3y + z = 11
-6 + 4y - 4z = 26
Adding these two equations, we get:
4y - 3z = 37
Now, multiply the first equation by 3 and add it to the third equation:
6 + 3y + 3z = 6
-3 + 2y - 2z = -13
Adding these two equations, we get:
3y + z = -7
Now we have the system of equations:
-2y - z = 7
4y - 3z = 37
3y + z = -7
By solving this system, we find that there are infinitely many solutions (C).