Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties $P_{1}$ , $P_{2}$ and $P_{3}$ with system relations $R_{1}$ , $R_{2}$ , $R_{3}$ , $R_{4}$ .
$Properties:$
$P_{1}$ : Linear but NOT time-invariant
$P_{2}$ : Time-invariant but NOT linear
$P_{3}$ : Linear and time-invariant
$Relations:$
$R_{1} : y (t) = t^{2} x (t)$
$R_{2} : y (t) = t | x (t) |$
$R_{3} : y (t) = | x (t) |$
$R_{4} : y (t) = x (t - 5)$

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Solution

$(P_{1}, R_{1}), (P_{2}, R_{3}), (P_{3}, R_{4})$

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