Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?
To determine if the linear system has an infinite number of solutions, we need to look for graphs that are coincident or overlapping.
First, we'll put the given equations in slope-intercept form (y = mx + b):
Equation 1: −2x + y = 6
y = 2x + 6
Equation 2: 4x − 2y = −12
-2y = -4x - 12
y = 2x + 6
We can see that the two equations have the same slope (2) and the same y-intercept (6), so they are coincident lines.
Thus, the graph that shows that the linear system has an infinite number of solutions is the one where the two lines overlap or coincide with each other.