Cumulative Standards Review
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Choose a test point which does not lie on either boundary line and substitute it into the given inequality to check which regions to shade. The solution will be the intersection, or overlap, of the shaded regions.
G
Graphing a single inequality involves two main steps.
The system's solution set will be the intersection of the shaded regions in the graphs of (I) and (II).
In the exercise the boundary lines are already given. Let's draw them!
Before we can shade the solution set for each inequality, we need to determine on which side of the plane their solution sets lie. To do that, we will need a test point that does not lie on either boundary line.
It looks like the point ( 0, 0) would be a good test point. We will substitute this point for x and y in the given inequalities and simplify. If the substitution creates a true statement, we shade the same region as the test point. Otherwise, we shade the opposite region.
| Information | Inequality (I) | Inequality (II) |
|---|---|---|
| Given Inequality | y≤-7x+12 | y≤ - 2/3x-2/3 |
| Substitute (0,0) | 0? ≤-7( 0)+12 | 0? ≤- 2/3( 0)-2/3 |
| Simplify | 0≤12 | 0≰- 2/3 |
| Shaded Region | same | opposite |
For Inequality (I) we will shade the region containing our test point, or below the boundary line. For Inequality (II), however, we will shade the region opposite the test point, or below the boundary line.
The shaded region corresponds to region B on the given graph. Therefore, our answer is G.