Questions: 4x + 9y = 12 -2x + y = -6

4x + 9y = 12
-2x + y = -6

Transcript text: 1.11) $\left\{\begin{array}{l}4 x+9 y=12 \\ -2 x+y=-6\end{array}\right.$

Solution

Solution Steps

Step 1: Find the equations from the first graph

The first graph shows two intersecting lines. One line passes through points (0,2) and (1,1). The slope is (1-2)/(1-0) = -1. The equation of the line is y = -x + 2. The second line passes through the points (0,-1) and (1, -2). The slope is (-2 - -1)/(1-0) = -1. The equation of this line is y = -x -1.

Step 2: Classify the system of equations

The system of equations y = -x + 2 and y = -x - 1 is inconsistent because the slopes are equal but the y-intercepts are different. Therefore, the lines are parallel and there is no solution.

Step 3: Find the solution from the second graph

The two lines intersect at the point (3,0). Therefore the solution to the system is x=3 and y=0.

Final Answer:

1.10) a. y = -x + 2 and y = -x - 1 b. Inconsistent 1.11) x = 3, y = 0

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The data sets give the number of platinum albums for the five male artists and the five female artists in a country with the most platinum albums through a recent year. (Platinum albums sell one million units or more.) Complete parts (a) through (d) below. Male Artists with the most platinum albums Artist Platinum Albums Artist 1 142 Artist 2 97 Artist 3 85 Artist 4 82 Artist 5 69 Female Artists with the most platinum albums Artist Platinum Albums Artist 1 67 Artist 2 62 Artist 3 56 Artist 4 56 Artist 5 46 a. Without calculating, which data set has the greater mean number of platinum albums? Explain your answer. A. Female artists have the greater mean number of platinum albums because all of the data items for the women are less than the greatest data item for the men. B. Female artists have the greater mean number of platinum albums because all of the data items for the women are greater than the greatest data item for the men. C. Male artists have the greater mean number of platinum albums because all of the data items for the men are greater than the greatest data item for the women. D. Male artists have the greater mean number of platinum albums because all of the data items for the men are less than the greatest data item for the women. b. Verify your conjecture from part (a) by calculating the mean number of platinum albums for each data set. Mean (Male artists) =95 Mean (Female artists) =57.4 (Round to two decimal places as needed.) c. Without calculating, which data set has the greater standard deviation? Explain your answer. A. Male artists have the greater standard deviation because there is a greater spread in the data for men. B. Male artists have the greater standard deviation because there is a lower spread in the data for men. C. Female artists have the greater standard deviation because there is a greater spread in the data for women. D. Female artists have the greater standard deviation because there is a lower spread in the data for women.

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