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