2. \( y>-2 \) \( y \leq x+9 \)

It seems that the system of inequalities provided cannot be solved using the standard methods for equations. However, I can help you analyze the inequalities step by step. ### Given Inequalities: 1. \( y > -2 \) 2. \( y \leq x + 9 \) ### Step 1: Analyze the first inequality The first inequality \( y > -2 \) indicates that the value of \( y \) must be greater than -2. This represents a horizontal line at \( y = -2 \) and includes all values above this line. ### Step 2: Analyze the second inequality The second inequality \( y \leq x + 9 \) indicates that the value of \( y \) must be less than or equal to the line represented by \( y = x + 9 \). This line has a slope of 1 and a y-intercept of 9. ### Step 3: Graphical Representation To visualize the solution, we can plot both inequalities on a coordinate plane: - The line \( y = -2 \) will be a dashed line (since \( y \) is not equal to -2). - The line \( y = x + 9 \) will be a solid line (since \( y \) can equal \( x + 9 \)). ### Step 4: Determine the feasible region The solution to the system of inequalities will be the region where: - Above the line \( y = -2 \) - Below or on the line \( y = x + 9 \) ### Conclusion The solution set consists of all points \( (x, y) \) that satisfy both inequalities. The feasible region is bounded by the two lines, where \( y \) is greater than -2 and less than or equal to \( x + 9 \). If you need further assistance or a specific calculation, please let me know!