Which graph represents the system of inequalities why is less than or equal to -3x - 2 Y is greater than or equal to 2x + 1
Since we have two inequalities, we can graph them separately and find the overlapping region to represent the system of inequalities.
First, let's graph y ≤ -3x - 2:
To graph y ≤ -3x - 2, we can start by graphing the line y = -3x - 2.
Plot two points on the line, for example, when x = 0, y = -2 and when x = 1, y = -5.
Next, we need to determine whether the line should be solid or dashed. Since it is "less than or equal to," we use a solid line.
Now, shade the area below the line to represent y ≤ -3x - 2.
Graph of y ≤ -3x - 2:
(Shaded region below the line)
y-axis
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Next, let's graph y ≥ 2x + 1:
To graph y ≥ 2x + 1, we can start by graphing the line y = 2x + 1.
Plot two points on the line, for example, when x = 0, y = 1 and when x = 1, y = 3.
Next, we need to determine whether the line should be solid or dashed. Since it is "greater than or equal to," we use a solid line.
Now, shade the area above the line to represent y ≥ 2x + 1.
Graph of y ≥ 2x + 1:
(Shaded region above the line)
y-axis
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To represent the system of inequalities, we find the overlapping region of the shaded regions from both graphs:
Overlapping region of shaded regions:
(Area shaded below the first line and above the second line)
y-axis
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This overlapping region represents the system of inequalities.