2. solve the following system. show all your work. {3x - 2y + 2z = 30 {-x + 3y - 4z = -33 {2x - 4y + 3z = 42

From the system of equations, we have 3 unknowns and 3 equations. Therefore, it can be solved. 

3x - 2y + 2z = 30  (1)
-x + 3y - 4z = -33  (2)
2x - 4y + 3z = 42   (3)

We can write equation 2 x as a function of y and z and substitute the new equation to the other equations.
x =3y - 4z + 33  (2)

3 (3y - 4z + 3) - 2y + 2z = 30  (1)
2 (3y - 4z + 3) - 4y + 3z = 42   (3)

We simplify and solve the equations and we get values,

x = 4
y = -7
z = 2