Which of these graphs show that the linear system -2x+y=6 and 4X-2y=-12 has an infinite number of solutions

Answer 1

To determine if a linear system has an infinite number of solutions, we need to check if the two equations are equivalent (i.e., they represent the same line).

Let's plot these two equations:

Graph 1:

-2x + y = 6

This equation can be rewritten as y = 2x + 6.

Graph 2:

4x - 2y = -12

This equation can be rewritten as y = 2x + 6.

Both equations have the same slope-intercept form, y = 2x + 6. Therefore, the two equations are equivalent, meaning that they represent the same line.

Since the two equations represent the same line, the linear system has an infinite number of solutions.

To summarize, both graphs show that the linear system -2x + y = 6 and 4x - 2y = -12 has an infinite number of solutions.