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Graph the solution of the system of inequalities and find the coordinates of all vertices for
x + 2y ≤ 14
3x - y ≥ 0
x - y ≥ 2
Solution:
For x + 2y ≤ 14, we need to rewrite the given equation into slope-intercept form as follows
Since
the sign of inequality is less than or equal to, then all points along the line
are included in the solution. If x = 0 and y = 0, then the given
equation reduces to 0 ≤ 14 which is correct and that point is
included in the solution.
For 3x - y ≥ 0, we need to rewrite the given equation into slope-intercept form as follows
If you divide both sides of the equation by a negative number, then the sign of inequality will be reversed. Since the sign of inequality is greater than or equal to, then all points along the line are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≥ 0 which is correct and that point is included in the solution.
For x - y ≥ 2, we need to rewrite the given equation into slope-intercept form as follows
If you divide both sides of the equation by a negative number, then the sign of inequality will be reversed. Since the sign of inequality is greater than or equal to, then all points along the line are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≥ 2 which is not correct and that point is not included in the solution. Therefore, the graph of a set of linear inequalities is
The vertices of the graph are (-1, -3) and (6, 4) that are located at the intersection of the three shaded regions bounded by three lines.
For 3x - y ≥ 0, we need to rewrite the given equation into slope-intercept form as follows
If you divide both sides of the equation by a negative number, then the sign of inequality will be reversed. Since the sign of inequality is greater than or equal to, then all points along the line are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≥ 0 which is correct and that point is included in the solution.
For x - y ≥ 2, we need to rewrite the given equation into slope-intercept form as follows
If you divide both sides of the equation by a negative number, then the sign of inequality will be reversed. Since the sign of inequality is greater than or equal to, then all points along the line are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≥ 2 which is not correct and that point is not included in the solution. Therefore, the graph of a set of linear inequalities is
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