Answer:
a) correct system of equations is B.
b) ordered pair is (6, 13)
each solo act is 6 minutes long
each ensemble act is 13 minutes long
Explanation:
Let's first take a look at the first talent show. There will be 12 solo acts and 2 ensemble acts and the total running time is 98 minutes. It is given that each solo act lasts x minutes and ensemble act y minutes.
Knowing this, we can write the first equatuon:
12x + 2y = 98
Now, the second show will consist of 6 solo acts and 2 ensemble acts lasting 62 minutes in total. That gives us enough information to write the second equation:
6x + 2y = 62
So, this gives us a system of equations:
12x + 2y = 98
6x + 2y = 62
In order to solve it, we can use a method of elimination which is adding up or subtracting two equations in order to eliminate one unknown. Since in both equations we have 2y, we will subtract them so that 2y and 2y cancel each other out:
12x + 2y - (6x + 2y) = 98 - 62
12x + 2y - 6x - 2y = 36
6x = 36
x = 6
Eliminating y from the system left us only with one unknown (x) which was easy to solve.
Now that we know the value of x, we can plug it back into any of the first two equations and solve for y:
12x + 2y = 98
72 + 2y = 98
2y = 26
y = 13
Now, we know both values, so the ordered pair (x,y) is (6,13)
