The system of inequalities y ≥ —4х — 4 and 1x is graphed. Which region is the feasible region (solution)?
The feasible region or solution of a system of inequalities is the region where all the inequalities are satisfied.
In this case, the given inequalities are y ≥ —4x — 4 and x is graphed. To find the feasible region, we need to shade the region that satisfies both inequalities.
First, let's graph the line y = —4x — 4. We can plot a few points and draw a line through them:
x | y = -4x - 4
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0 | -4(-0) - 4 = -4
1 | -4(1) - 4 = -8
-1 | -4(-1) - 4 = 0
Plotting these points and drawing a straight line through them, we get:
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Next, we need to determine which side of the line satisfies the inequality y ≥ —4x — 4. We can test a point on either side of the line to determine which side to shade.
For example, let's test the point (0,0) which is on the lower side of the line.
Plugging the coordinates (x = 0, y = 0) into the inequality, we get:
0 ≥ -4(0) - 4
0 ≥ -4 - 4
0 ≥ -8
Since 0 is greater than or equal to -8, the lower side of the line satisfies the inequality.
Therefore, the feasible region or solution is the lower side of the line y = —4x — 4.
Graphically, it would be the region below the line.