Final answer:
To identify which system of equations a graph represents, one must differentiate between linear and quadratic functions and then analyze the shape and slope. Linear equations form straight lines while quadratic equations form parabolas. Without the actual graph, it isn't possible to give a definitive answer.
Step-by-step explanation:
The question asks which system of equations a given graph represents. To determine this, we need to understand the properties of linear equations and quadratic equations. A linear equation is of the form y = mx + b, where m is the slope and b is the y-intercept, and it represents a straight line in a graph. A quadratic equation is of the form y = ax² + bx + c, which represents a parabolic curve.
Options (a), (c), and (d) propose linear equations, while option (b) presents a quadratic equation. For linear equations, if the slope m is positive, as seen in Figure 12.4, the line slopes upward to the right; if m = 0, the line is horizontal; and if m < 0, the line slopes downward to the right. A quadratic equation graph can be recognized by its characteristic parabolic shape.
To decipher which equation the graph represents, one must analyze the graph provided. If the graph shows a straight line with a positive, negative, or zero slope, it corresponds to a linear equation, and if it shows a parabola, it corresponds to a quadratic equation. Without the graph, we cannot give a definitive answer, but we can use this knowledge to match the graph to its equation when provided.