X+z=6 5y+9z=1 what is a possible way to eliminate the y term

Assuming that these two equations aren't being multiplied:

solve the second equation for y

5y+9z=1 5y=1-9z y = (1-9z) / 5

substitute y for 0

0 = (1-9z) / 5

5=1-9z

We could leave it like this, but I'm not going to because it feels so unfinished.

5-1=-9z

4=-9z

-4/9=z

x+z=6

x - (4/9) = 6

x=6 + (4/9)

x=58/9