Algebra 2 question, what is the value of z in the system of equations?

2x - y = -5

4x + 4y - 2z = 6

4x + 3z = 6

All of these equations have an x in them, so solve the first and third equations for their OTHER variable:

2x - y = -5

-y = -2x - 5

y = 2x + 5

4x + 3z = 6

3z = -4x + 6

z = (-4/3)x + 2

Plug these into the middle equation:

4x + 4(2x + 5) - 2((-4/3)x + 2) = -6

Now everything is in terms of x. Expand and simplify to solve for x:

4x + 8x + 20 + (8/3)x - 4 = -6

(44/3)x + 16 = -6

(44/3)x = -22

x = -22 * (3/44) = -3/2

Now that we have x, plug this into the third equation we re-wrote to find z:

z = (-4/3)(-3/2) + 2

Simplify:

z = 2 + 2 = 4

So, z = 4