To determine which points are solutions to the given system of linear inequalities based on a graph, you would need to check if each point satisfies all of the inequalities represented by the boundaries of the shaded regions in the graph.
Since I can't view the graph, I'll demonstrate how you could check each point theoretically. Usually, you would follow these steps:
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Identify Inequalities: From the graph, note the boundaries created by the lines. Determine if the inequalities are of the form \(y < mx + b\), \(y > mx + b\), etc., and whether the lines are solid or dashed (which indicates whether the boundary is included).
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Test Each Point: For each listed point, substitute the coordinates into the inequalities to see if they hold true.
For the points you've listed, you would want to check:
- Point (0,−2): Substitute \(x=0\) and \(y=-2\).
- Point (0,−1): Substitute \(x=0\) and \(y=-1\).
- Point (1,−2): Substitute \(x=1\) and \(y=-2\).
- Point (2,−1): Substitute \(x=2\) and \(y=-1\).
- Point (6,2): Substitute \(x=6\) and \(y=2\).
- Point (−4,−6): Substitute \(x=-4\) and \(y=-6\).
After testing each point against the inequalities derived from the graph, you will determine which points satisfy all inequalities and thus are solutions to the system.
If you could provide the specific inequalities or more context from the graph, I could help you more accurately identify the valid solutions.