Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

y ≥ −3x + 3
y is less than 3 over 2 times x minus 6

Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)

Part B: Is the point (−6, 3) included in the solution area for the system? Justify your answer mathematically. (4 points)

(10 points)

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The graph of y ≥ −3x + 3 will be a solid line with the equation y=−3x + 3, this solid line signifies that the value on this line is also included in the solution. Since the symbol is '≥' therefore the area above the line will have the solutions.

The graph of y<(3/2)x -6 will be a dashed line with the equation y=(3/2)x - 6, this dashed line signifies that there is no solution on the line. since the inequality symbol is '<' therefore, the area under the dashed line will have all the solutions.

The area where both shaded areas meet is the area that will have all the possible solutions.

PartB:

y ≥ −3x + 3

3 ≥ -3(-6) + 3

3 ≥ 18 + 3

Since the above inequality is not satisfied, (-6, 3) is not the solution to the system of inequalities.

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