Question

Determine if the system is inconsistent by graphing and finding the slope. y=2/3x+5

−4x+6y=12 (1 point) Responses

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the system is inconsistent, we need to graph both equations and see if they intersect at a single point (consistent) or are parallel lines (inconsistent).

First, let's graph the equation y=2/3x+5. The slope of this equation is 2/3.

Next, let's rearrange the second equation −4x+6y=12 in slope-intercept form. We get y = 2/3x + 2. By comparing the two equations, we can see that they have the same slope. This means that the lines are parallel.

Since the lines are parallel and do not intersect, the system is inconsistent.