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