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Graph the solution of the system of inequalities and find the coordinates of all vertices for
a. x + y ≤ 4
y ≥ x
b. 2x + 3y > 12
3x - y < 21
Solution:
a. For x + y ≤ 4, 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 ≤ 4 which is correct and that point is included in the solution.
For y ≥ x, the given equation is already written in slope-intercept form. 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. Therefore, the graph of a pair of linear inequalities is
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| Photo by Math Principles in Everyday Life |
The vertex of the graph is (2, 2) which is the intersection of two lines. It is also included in the solution.
b. For 2x + 3y > 12, we need to rewrite the given equation into slope-intercept form as follows
Since the sign of inequality is greater than, then all points along the line are not included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 > 12 which is not correct and that point is not included in the solution.
For 3x - y < 21, 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 less than, then all points along the line are not included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 < 21 which is correct and that point is included in the solution. Therefore, the graph of a pair of linear inequalities is
 |
| Photo by Math Principles in Everyday Life |
The vertex of the graph which is the intersection of two lines is not included in the solution.