Final answer:
To determine which system of linear inequalities is represented by a graph, we review the slope and y-intercept of the boundary lines and the shaded regions. By matching these properties to the options given, we identify the correct system.
Step-by-step explanation:
To determine which system of linear inequalities is represented by a graph, one must analyze the properties of the lines and shaded regions depicted in the graph. The inequalities y > x - 2 and x - 2y < 4 or y > x + 2 and x + 2y < 4 or y > x - 2 and x + 2y < 4 or lastly y > x - 2 and x + 2y < -4 represent four different systems.
By looking at the orientation of the shaded regions and the slope and y-intercept of the boundary lines in the graph, which can be found using the equation of a linear equation y = a + bx, where a represents the y-intercept and b the slope, we can identify which system of inequalities matches.
For example, if the line y = x - 2 is depicted as having a slope of 1 and y-intercept at -2 with the region above it shaded, it means y > x - 2. Similarly, if for the inequality x + 2y < 4, the line appears to have a slope of -0.5 (since 2y = -x + 4, y = -1/2x + 2) with the region below it shaded, this corresponds to the inequality given.
To identify the correct system, match the properties of the lines and shaded regions in the graph to those described by the options given.