$($a$)$ Consider a continuous$-$time system with input, $x(t),$ and output, $y(t).$

The input$-$output relationship for this system is

$y(t)=x^3(t)+3$

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

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

$[8$ marks$]$