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Graph the solution of the system of inequalities and find the coordinates of all vertices for
x ≥ 0
y ≥ 0
3x + 5y ≤ 15
3x + 2y ≤ 9
Solution:
For x ≥ 0, the given line is a vertical line in which all points along the line are included in the solution. However, all points at the right of the given line are included in the solution.
For y ≥ 0, the given line is a horizontal line in which all points along the line are included in the solution. However, all points above of the given line are included in the solution.
For 3x + 5y ≤ 15, 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 ≤ 15 which is correct and that point is included in the solution.
For 3x + 2y ≤ 9, 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 ≤ 9 which is correct and that point is included in the solution. Therefore, the graph of a set of linear inequalities is
The vertices of the graph are (0, 0), (0, 3), (1 2/3, 2) and (3, 0) that are located at the intersection of the four shaded regions bounded by four lines.
For y ≥ 0, the given line is a horizontal line in which all points along the line are included in the solution. However, all points above of the given line are included in the solution.
For 3x + 5y ≤ 15, 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 ≤ 15 which is correct and that point is included in the solution.
For 3x + 2y ≤ 9, 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 ≤ 9 which is correct and that point is included in the solution. Therefore, the graph of a set of linear inequalities is
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| Photo by Math Principles in Everyday Life |
The vertices of the graph are (0, 0), (0, 3), (1 2/3, 2) and (3, 0) that are located at the intersection of the four shaded regions bounded by four lines.