Answer
a) $12x+2y=90$
$\ \ \ \ 6x+2y=60$
b) Each solo act is 5 minutes. Each ensemble act is 15 minutes.
Work Step by Step
The time for the first show can be written as
$12x+2y=90$
The time for the second show can be written as
$6x+2y=60$
Multiply the second equation by -1. Add the two equations to eliminate y.
$12x+2y=90\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12x+2y=\ \ \ 90$
$6x+2y=60\ \ \ \ $multiply by -1$\ \ \ \ \underline{\ -6x-2y=-60}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6x\ \ \ \ \ \ \ \ \ \ =\ \ 30$
Solve for x, the length of each solo act.
$6x=30$
$6x\div6=30\div6$
$x=5$
Substitute 5 for x in either equation and solve for y, the length of each ensemble act.
$12(5)+2y=90$
$60+2y-60=90-60$
$2y=30$
$2y\div2=30\div2$
$y=15$
