Question

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points negative 2 comma negative 5 and 0 comma negative 4 and another line that passes through the points 0 comma 1 and 1 comma negative 1. One solution at (2, −3) One solution at (−3, 2) No solution Infinitely many solutions

Answer 1

To determine the number of solutions, the slopes of the given lines are calculated and compared. Since the slopes are different, the lines intersect at one point, indicating the system has exactly one solution.

Step-by-step explanation:

The number of solutions a system of linear equations has can be determined by looking at the slopes of the lines represented in the graph. If the slopes are different, the lines intersect at one point, and there is exactly one solution to the system. The two given lines pass through points (-2, -5) to (0, -4) and from (0, 1) to (1, -1), respectively. By calculating the slope of each line (rise over run), we can determine whether they are the same or different.

The slope of the first line is ((-4) - (-5)) / (0 - (-2)) = 1/2. The slope of the second line is ((-1) - 1) / (1 - 0) = -2. Because these slopes are different, the lines intersect at exactly one point, which means the system has one solution. The given solution at (2, -3) is that single point of intersection if the graph is accurately plotted to scale and the question reflects the actual intercept on the graph.