$($a$)$ Consider a discrete$-$time system with input, $x[n],$ and output, $y[n].$

The input$-$output relationship for this system is

$y[n]=2x[n]+1$

$($i$)$ Is the system linear? Justify your answer.

$($ii$)$ Is the system time$-$invariant? Justify your answer.

$[10$ marks$]$