Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y<-3 over 4x-1
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 (8, 10) included in the solution area for the system? Justify your answer
mathematically.

The point (5,-8) is not in the solution area.

40

Step-by-step explanation:

The given inequalities are

y < 4x - 8

y_> 5/2r+5

Part A

The graph is shown below. The shaded regions indicate where both inequalities hold.

Notice that when y changes sign, the sign of the inequality gets flipped. For example,

y< 4x - 8 becomes - y> -4x + 8.

Part B

Visually, the point (5, -8) is not included in the solution area.

Test the inequality y < 4x - 8 When x = 5, we should be in the shaded

area.

y< 4*8 8

y< 24

y< 24 is conditionally true.

Notice that y is below the red curve, which approaches O asymptotically from above.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

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