Your schoor's talent show will fleasure 10 solo acts and 2 ensemble acts. The show will last 90 minutes. The 5 solo performers judged best will give a repeat performance at a second 60 minute show, which will siso feature the 2 ensemble acts: Each solo act lasts x minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b)
a) Write a system of equations to model the situation.
2x + 10y = 90
2x + 5y = 60
2x + 10y = 60 2x + 5y = 90
10x + 2y = 90 5x + 2y - 60 C
10x + 2y = 60
OD
5x + 2y = 90
b) Solve the system from part (a).
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(Type an ordered pair.).
The correct system of equations to model the situation is:
2x + 10y = 90
2x + 5y = 60
To solve this system of equations, we can use the substitution method or the elimination method.
Using the elimination method, we can multiply the second equation by 2 to match the coefficients of x:
2x + 10y = 90
4x + 10y = 120
Subtracting the first equation from the second equation, we get:
(4x + 10y) - (2x + 10y) = 120 - 90
2x = 30
x = 15
Substituting the value of x into the first equation, we get:
2(15) + 10y = 90
30 + 10y = 90
10y = 60
y = 6
Therefore, the solution to the system of equations is (x, y) = (15, 6).