For a certain value of k

First, we evaluate the result of the equations without k. We get:

 

$$y = 6 x - 12, z = 22/3 - (7 x)/3$$

$$ x = 1/7 (22 - 3 z)$$

 

For $kx+z=3$ to agree with these equations, we need to solve for k.

 

Solving for k in terms of z, $$ k = \frac{ 7 (z - 3)}{3 z - 22}.$$

 

However, we want $kx+z \ne 3.$ 

 

See if you can work more on this on your own!