Which of the following systems of inequalities matches the graph shown? yleqslant 2x-8 AND ygeqslant 7x+3 yleqslant x+4 AND ygeqslant 2x -5 ygeqslant -2x+4 AND yleqslant x-5 yleqslant -2x+4 AND ygeqslant x-5

To determine which system of inequalities matches the graph, we need to find the equations of the lines and then determine the correct inequality signs based on the shaded areas.Step 1: Find the equation of the blue line.The blue line passes through the points (0,3) and (6,9). To find the slope (m) of the line, we use the formula: Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. We'll use the point (0,3): Since the area above the blue line is shaded, the inequality for the blue line should be: Step 2: Find the equation of the orange line.The orange line passes through the points (0,0) and (6,-10). To find the slope (m) of the line, we use the formula: Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation. We'll use the point (0,0): Since the area below the orange line is shaded, the inequality for the orange line should be: Step 3: Match the equations and inequalities to the given options.The correct system of inequalities must match the equations we found with the appropriate inequality signs. The equations we found are: None of the given options exactly match the equations we found. However, we need to consider that the intersection point given in the picture details (-4,4) does not match the intersection point that would result from the equations we derived. This suggests there may be an error in the picture details or in the interpretation of the graph.Given the intersection point (-4,4), we can check which lines would actually intersect at this point. The line with a positive slope passing through (0,3) would be y = x + 3, and the line with a negative slope passing through (0,0) would be y = -\frac{5}{3}x. However, these lines would not intersect at (-4,4).Let's assume the intersection point is correct and find the equations based on that point and the given points the lines pass through.For the blue line passing through (0,3) and intersecting at (-4,4), the slope is: This slope does not match the slope we calculated earlier, so there is a discrepancy. However, if we proceed with the intersection point, the equation of the blue line would be: For the orange line passing through (0,0) and intersecting at (-4,4), the slope is: The equation of the orange line would be: Now, let's match these equations with the inequalities and the shaded areas:- The blue line's area is shaded above, so the inequality should be .- The orange line's area is shaded below, so the inequality should be .None of the given options match these inequalities. Given the discrepancy and the information provided, it is not possible to accurately determine which system of inequalities matches the graph shown. There seems to be an error in the provided picture details or the options given.