## Linear Systems

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 .
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