Solve the system of equations
`{(|x-1|+|y-2|=1),(y=2-|x-1|):}`

Explanation

On substituting `|x-1|=2-y` from second equation in first equation of this system we get
`2-y+|y-2|=1`
Now consider the following cases
If `yge2`
then `2-y+y-2=1implies0=1`
No value of `y` for `yge2`
If `ylt2`
then `2-y+2-y=1hArry=3/2` which is true.
From the second equation of this system
`3/2=-|x-1|`
`implies|x-1|=1/2impliesx-1=+-1/2`
`impliesx=1+-1/2impliesx=1/2,3/2`
Consequently, the set of all solutions of the original system is the set of pairs `(x,y)` where `x=1/2,3/2` and `y=3/2`.