We have two equations

`3x+y=x+3=>2x+y=3`

`x-1=2y-2x=>3x-2y=1`

Multiply the top equation by 2 we get the follwing system

`4x+2y=6`

`3x-2y=1`

add we get `7x=7=>x=1`

Plug in the first equation we get `2+y=3=>y=1`

Hence x=1 and y=1

We have two equations

`3x+y=x+3=>2x+y=3`

`x-1=2y-2x=>3x-2y=1`

Multiply the top equation by 2 we get the follwing system

`4x+2y=6`

`3x-2y=1`

add we get `7x=7=>x=1`

Plug in the first equation we get `2+y=3=>y=1`

Hence x=1 and y=1