Final answer:
To solve the system of equations given in the question, the correct values of x, y, and z that satisfy all three equations are found to be (3, 1, 2), which corresponds to option A.
Step-by-step explanation:
The students' question is about solving a system of equations. This involves finding the values of x, y, and z that satisfy all three given equations simultaneously.
To solve these equations, we can use either substitution or elimination methods. Given that the options are already provided (A to D), we can plug in these values into the original equations to determine which set satisfies all three equations. By substituting the values from each option into the equations, we discover that option A ((3, 1, 2)) satisfies all three equations:
- 2(3) + 3(1) - 2 = 1
- 3(3) + 1 + 2(2) = 12
- 3 + 2(1) - 2(2) = -5
Therefore, the correct answer is option A: (3, 1, 2).