If c is the line segment connecting (x1,y1) to (x2,y2), show that the line integral of xdy-ydx=x1y2- is in a chapter about green's theorem don't answer if you really don't know or understand this kind of stuff.

Green's theorem doesn't really apply here. GT relates the line integral over some *closed* connected contour that bounds some region (like a circular path that serves as the boundary to a disk). A line segment doesn't form a region since it's completely one-dimensional.

At any rate, we can still compute the line integral just fine. It's just that GT is irrelevant.

We parameterize the line segment by




with . Then we find the differential:




with .

Here, the line integral is







as required.

Option B - graphing is the correct answer.

Step-by-step explanation:

To solve a system of inequalities we need graphing. Inequality tells us about the relative size of two values. When we graph the x and y co-ordinates, the solution is not the drawn line, but the area of the coordinate plane that satisfies the inequality. In inequalities, multiple solutions can be possible.

Plug and chug method does not a complete solution, it only tells where a point belongs. Guess and check does not apply here.