# Linear Systems

1. Apr 1, 2005

### alyssa

Linear Systems

1 . Use your graphing calculator and linear regression to find the best fit line for each of these data tables .

A ) x 1.5 0.8 3.5 8.5 6.8 7.5
Y 7.0 5.9 11.9 24.5 21.5 22.5

B ) x 12 9 3 11 7 2
Y 8 45 120 20 70 133

2 . Two large tanks are sitting next to one another . When an engineer started timing , the first tank had 2400L of oil in it while the second tank had only 985L in it . However , the first was losing oil at a rate of 35L every 8 minutes while the second tank was gaining oil at the rate of 42L every 5 minutes . Model the amount of oil in each tank using a linear equation . Carefully define the variables you use . After how many minutes will the two tanks have the same amount of oil in them ?

A local high school produced a special yearbook for the graduating class . The following table was prepared by the business manager of the school .

Number of Yearbooks Sold Production Cost Sales Revenue
( N ) ( C in $) ( S in$ )

15 682.50 187.50
76 1262.00 950.00
124 1718.00 1550.00
255 2962.50 3187.50
312 3504.00 3900.00

1 . Use linear regression to find C as a function of N .

2 . Use linear regression to find S as a function of N .

3 . Write these two equations as a linear system using the variables x and y .

4 . Use your calculator to find the break-even point . Copy down the window settings that you used .

5. Use either substitution or elimination to solve the linear system that you developed in # 3 . Show all of your steps .

6. Use the linear system to calculate the profit or loss when 120 , 240 , 318 , and 146 books are sold . Show your calculations .

2. Apr 2, 2005

### xanthym

If you need Linear Regression capabilities, try the following Web Site:
http://www.arachnoid.com/polysolve/
Allow time to load program, scroll down to page bottom, input data pairs in data area like example, select "Polynomial" regression of Degree "1" for linear fit, regression equation is given below graph in "Results" area.

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Last edited: Apr 2, 2005
3. Apr 2, 2005