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3 years ago

Y ≥ 12x – 1 y < 43x – 2

Mathematics

1 answer:

kondaur [170]3 years ago

5 0

Answer:

Step-by-step explanation:

The solution to this problem is a graph.

Graph y ≥ 12x - 1: this is a straight solid line with slope 12 and y-intercept -1. Due to the presence of the ≥ operator, we must shade (darken) the entire area above this line.

Next, graph y < 43x – 2 using a dashed line (due to the < operator): The slope is 43 and the y-intercept is -2.

Determine where the two lines intersect, either from the graph or algebraically. If algebraically:

equate the two givens:

y = 12x - 1 = y = 43x – 2, which simplifies first to:

12x - 1 = 43x - 2, and second to

1 = 43x - 12x = 31x, which results in x = 1/31.

Substituting 1/31 for x in the first equation, we get:

y = 12(1/31) - 1, or y = 12/31 - 1, or y = 12/31 - 31/31, or y = 19/31

The two graphs intersect at (1/31, 19/31)

Shade (darken) the area beneath (under) the dashed line y < 43x – 2.

The solution is the area that you have darkened twice.

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Answer:

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