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please show detailed solution

for the problems shown will upvote

7.1 Use the superposition and time-delay properties to find the $z$-transforms of the following signals $x_{1}[n]x_{2}[n]x_{3}[n]x_{4}[n] =δ[n]=δ[n−1]=δ[n−7]=2δ[n]−3δ[n−1]+4δ[n−3] $ 2 Use the superposition and time-delay properties of (7.3.1) and (7.3.4) to determine the $z$-transform $Y(z)$ in terms of $X(z)$ if $y[n]=x[n]−x[n−1]$ and in the process show that for the first difference system, $H(z)=1−z_{−1}$.