Graph the solution set of each system of inequalities. y≥3x y≥2
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Step 1: Identify the inequalities in the system. The system consists of two inequalities: and .
Step 2: Graph the first inequality . Start by graphing the boundary line , which is an exponential function. Plot points for several values of to get the shape of the curve, such as , and so on. Since the inequality is , shade the region above the curve.
Step 3: Graph the second inequality . This is a horizontal line at . Since the inequality is , shade the region above this line.
Step 4: Determine the solution set by finding the intersection of the shaded regions from both inequalities. The solution set is where the shaded region from overlaps with the shaded region from .
Step 5: Clearly mark the solution set on the graph. This is the region that satisfies both inequalities, and it will be the area above both the curve and the line .
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