Final answer:
The system of linear equations represented by the graph is option C: y = x - 3 and y = -4x + 2.
Step-by-step explanation:
The system of linear equations represented by the graph is option C: y = x - 3 and y = -4x + 2.
To determine the correct system of equations, we need to find the equations of the two intersecting lines on the graph. From the graph, we can see that the first line has a negative slope and intersects the y-axis at 2. This equation can be written as y = -4x + 2. The second line has a positive slope and intersects the y-axis at -3. This equation can be written as y = x - 3. Therefore, option C matches the graph.
The question is asking which system of linear equations is represented by two lines intersecting in the fourth quadrant on a graph. To determine which system matches the description, we need to consider the slopes and y-intercepts of the lines in each option.
From the description that they intersect in the fourth quadrant, we know that one line should have a positive slope, and the other should have a negative slope since they must intersect from opposite directions.