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.
