`2x + 4y + z = 1, x - 2y - 3z = 2, x + y - z = -1` Solve the system of linear equations and check any solutions algebraically.

From the third equation `z=x+y+1.` Substitute it into the first two equations and obtain

`2x+4y+x+y+1=1,` or `3x+5y=0,`

and

`x-2y-3x-3y-3=2,` or `2x+5y=-5.`

Now subtract these two equations to eliminate `y:`

`x=5.`

Now `y=-3/5 x=-3` and `z=x+y+1=3.`

The answer: `x=5,` `y=-3,` `z=3.` Check the solution:

`2x+4y+z=10-12+3=1` (true),
`x-2y-3z=5+6-9=2` (true),
`x+y-z=5-3-3=-1` (true).