Answer: Choice D
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Explanation:
Start by graphing the system of equations
[tex]\begin{cases}x-y = 6\\2x+5y = -4\\ x = -1\end{cases}[/tex]
This is represented as the boundary lines. The first two equations produce solid boundary lines. The last equation makes a dashed boundary line. We use solid boundary lines whenever "or equal to" is involved with the inequality sign.
Note how 7 separate regions result from the intersecting lines. Check out the diagram below to see the different regions.
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To graph [tex]x-y \le 6[/tex] which is the same as [tex]y \ge x-6[/tex], we will shade in regions 1, 2, 4 and 5. All of these regions are above the boundary line y = x-6
Ignore any other region (3,6, and 7) since they don't make the first inequality true.
Of regions 1, 4, 5 and 6, only regions 4 and 5 are below the boundary line 2x+5y = -4. So we cross off regions 1 and 6.
We're now down to just two regions: 4 and 5
We cross off region 5 because it is not to the right of the vertical line x = -1
All that's left is region 4. Any point in region 4 makes all of the three original inequalities true.
So the solution will only have region 4 shaded like choice D shows.
