Final Answer:
c) Infinitely many solutions These lines are parallel but have different y-intercepts and opposing inequality signs.
Explanation:
The system of inequalities includes two lines with inequalities representing y as a function of x. Graphing these inequalities, you'll notice that they form parallel lines with different y-intercepts and the same slope, one with a slope of 1/3 and a y-intercept of 5, and the other with a slope of -1/3 and a y-intercept of -1. Since they are parallel and have opposite inequality signs, they shade regions on the graph that are not overlapping, resulting in an infinite number of solutions.
This happens because any x, y pair within the graphed area will satisfy both inequalities simultaneously, providing an infinite number of possible solutions.
The inequalities y < 1/3x + 5 and y > -1/3x - 1 are represented by lines on a coordinate plane. The line for y < 1/3x + 5 has a slope of 1/3 and a y-intercept at (0, 5), while the line for y > -1/3x - 1 has a slope of -1/3 and a y-intercept at (0, -1). These lines are parallel but have different y-intercepts and opposing inequality signs.
When graphed, they shade regions on the plane that don't overlap, indicating that there's an infinite number of coordinate points within the shaded regions that satisfy both inequalities simultaneously. Thus, the system of inequalities has infinitely many solutions.