How do you graph the system of inequalities #Y ≥ - 5#, #Y ≤ 2x + 5#, #Y ≤ -2x + 5#?
Please see below.
For drawing the graph of a linear inequality, one needs to first draw the graph of the equation (i.e. with 'equal(=)' sign), which is a straight line.
Now this line divides the Cartesian Plane in three parts - (a) the line itself, on which every point satisfies the equality; (b) this line divides plane in two parts, and in one of them the function will satisfy 'greater than' condition and in the other, it will satisfy 'less than' condition.
For graphing, one may shade the required region. The line in such cases may be shown as 'dotted' indicating points on the line are 'not included'.
For condition 'greater than or equal to', it will be the line along with the region in which it is 'greater than' and in such cases line is shown as 'thick line' and the region representing 'greater than' will be shaded. The line is drawn as thick to indicate that points on the line are included in solution set.
For example, in
Similarly draw graphs of
The graphs should appear as follows:
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To graph the system of inequalities (y \geq -5), (y \leq 2x + 5), and (y \leq -2x + 5), follow these steps:
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Graph the line (y = -5). This is a horizontal line passing through the point (0, -5). Since (y) is greater than or equal to -5, shade the region above the line.
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Graph the line (y = 2x + 5). This is a line with a slope of 2 and a y-intercept of 5. Plot the y-intercept at (0, 5), and use the slope to find additional points. Since (y) is less than or equal to 2x + 5, shade the region below the line.
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Graph the line (y = -2x + 5). This is a line with a slope of -2 and a y-intercept of 5. Plot the y-intercept at (0, 5), and use the slope to find additional points. Since (y) is less than or equal to -2x + 5, shade the region below the line.
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The solution to the system of inequalities is the overlapping shaded region where all three inequalities are satisfied. This region represents the set of points that satisfy all three conditions simultaneously.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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