The figure shows the flow of traffic $($in vehicles per hour$)$ through a network of streets.

$($a$)$ Solve this system for $x_i,i=1,2,$dots,$5.($If the system has an infinite number of solutions, express $x_1,x_2,x_3,x_4,$ and $x_5$ in terms of the parameters $s$ and $t.)$

$($b$)$ Find the traffic flow when $x_3=0$ and $x_5=90.$

$(x_1,x_2,x_3,x_4,x_5)=$

$($c$)$ Find the traffic flow when $x_3=x_5=80.$

$(x_1,x_2,x_3,x_4,x_5)=$