# Chapter 6 - Systems of Equations and Inequalities - 6-3 Solving Systems Using Elimination - Practice and Problem-Solving Exercises - Page 378: 13

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. $12(5)+2y=90$ $60+2y-60=90-60$ $2y=30$ $2y\div2=30\div2$ $y=15$

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