Question15)
Studdy Solution
STEP 1
1. We are given a system of linear inequalities.
2. We need to find the solution set that satisfies both inequalities simultaneously.
3. The solution set will be a region on the Cartesian plane.
STEP 2
1. Graph the inequality .
2. Graph the inequality .
3. Determine the region that satisfies both inequalities.
4. Describe the solution set.
STEP 3
Graph the inequality :
1. Start by graphing the line . This is the boundary line.
2. Since the inequality is strict (), use a dashed line to indicate that points on the line are not included in the solution.
3. Choose a test point not on the line (commonly the origin, , if it is not on the line) to determine which side of the line to shade.
4. Substitute the test point into the inequality. If true, shade the region containing the test point; otherwise, shade the opposite region.
STEP 4
Graph the inequality :
1. Start by graphing the line . This is the boundary line.
2. Since the inequality is strict (), use a dashed line to indicate that points on the line are not included in the solution.
3. Choose a test point not on the line (commonly the origin, , if it is not on the line) to determine which side of the line to shade.
4. Substitute the test point into the inequality. If true, shade the region containing the test point; otherwise, shade the opposite region.
STEP 5
Determine the region that satisfies both inequalities:
1. Identify the region where the shaded areas from both inequalities overlap.
2. This overlapping region represents the solution set for the system of inequalities.
STEP 6
Describe the solution set:
1. The solution set is the region on the Cartesian plane where both inequalities are satisfied.
2. It is the intersection of the two shaded regions from the previous steps.
The solution set is the region where the shaded areas from both inequalities overlap on the Cartesian plane.
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