Which region in the graph below is the solution of the system of inequalities given below?

Option C: Region 2 is the solution to the system of inequalities

Explanation:

The system of inequalities is and

Let us substitute the coordinate in the inequality , we get,

Hence, the inequality becomes true.

So, let us shade the region that contains the point

And hence the shaded portion comes under the region 2 and region 3.

Now, let us substitute the coordinate in the inequality , we get,

Hence, the inequality becomes true.

So, let us shade the half that contains the point

And hence the shaded portion comes under the region 1 and region 2.

The solution of the system of inequalities is the intersection of the regions of the two inequalities.

Hence, the two inequalities intersect at the region 2.

Therefore, Region 2 is the solution to the system of inequalities.

Thus, Option C is the correct answer.

answer: sensy

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."