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**Unformatted text preview: **TI-83/4: Finding Points of Intersection
At a certain show at the Performing Arts Center, there are two types of seating available. General admission seating
tickets cost $10 each, and reserved seating cost tickets cost $18.
At last night’s performance there were a total of 200 people in attendance, and a total of $2640 was collected from
ticket sales. If we let x represent general admission tickets and y represent reserved seating, we can write down two
equations that describe the given information: x+ y = 200 10x + 18y = 2640
There are various algebraic techniques for solving this system. From your previous algebra classes you should
already be familiar with both the substitution method and the elimination method for solving linear systems. This
handout deals with calculator techniques.
We must first graph each equation using a suitable window, and to do this we need to solve each equation for y: y 1 = 200 − x
y2 = 2640 − 10x
18 To choose a suitable window, let’s construct a table representing extreme values for each variable. y = 200 − x
x
0
200 y
200
0 y= 2640 − 10x
18 x
0
264 y
146.7
0 Looking at these numbers, I will use xmin=0, xmax=300, ymin=0, ymax=300 as my window settings. Point P is the intersection of these graphs, and represents
the solution to the system. To find the coordinates of P: When we do this we get the point (120, 80) , which means that 120 general admission tickets and 80 reserved seating tickets were sold. We should now verify that these numbers satisfy both equations: (120) + (80) = 200
10(120) + 18(80) = 2640 ...

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