Question

Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)

Answer 1

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

Let's rearrange the first equation −2x + y = 6:

y = 2x + 6

Now, let's rearrange the second equation 4x − 2y = −12:

-2y = -4x - 12
y = 2x + 6

Both equations can be simplified to y = 2x + 6, which means the two equations represent the same line.

Therefore, the graphs of the linear system −2x+y=6 and 4x−2y=−12 would show a set of coinciding lines or one line on top of another, indicating an infinite number of solutions.

This can be represented by the graph:

Graph:
y = 2x + 6