Final answer:
The question involves analyzing graphs to match them with a system of linear equations, focusing on characteristics like slope and y-intercept. The correct graph will show how the lines interact, whether intersecting at a point, being parallel, or coinciding, indicating one, no, or infinite solutions, respectively.
Step-by-step explanation:
The question pertains to systems of linear equations and their graphical representation. To determine which graph represents the system of equations, we must analyze the lines depicted in the graphs. The key characteristics of a line in a graph are its slope and its y-intercept. A graph that represents a system of equations will display lines that either intersect at a single point (one solution), are parallel (no solution), or coincide (infinitely many solutions).
For the provided plots, we need to identify which graph corresponds to the system by examining the points through which the lines pass. The given points also allow us to calculate the slope of the lines. The slope is found using the formula (change in y)/(change in x), and the y-intercept is seen where the line crosses the y-axis (where x=0). Comparing these calculations with the graph will help us determine the correct one.
Once we've identified the corresponding graph, we can find the solution to the system of equations by locating the point of intersection if there is one. This point will have coordinates (x, y) that satisfy both equations simultaneously. If the lines are parallel, there is no intersection and therefore no solution. If the lines overlap entirely, there are infinitely many solutions.