Solve these systems for (x, y, z)

-x+y+z=4

-x+2y-3z=-6

2x-4y+8z=18

Multiply the first equation by - 1 and add it to the second one, getting

y-4z=-10

Multiply the first equation by 2 and add it to the third one, getting - 2y+10z=26

As you can see, we eliminated x and turned it into two equations with 2 variables.

Multiply the first new equation by 2 and add it to the second one to get

2z=6 and z=3. Substitute it in to - 2y+10z=26 to get y=2 and substitute it into - x+y+z=4 to get x=1