Please help me im stuck .

Choice A) Empty set

This is another way of saying "no solutions"

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Explanation:

Your teacher made a typo. The given inequalities will have boundary lines that both have positive slopes, not negative slopes. So the boundary lines should go uphill as you move from left to right.

See the diagram below to see what the graph should look like.

The upper dashed line is y = (1/2)x+3. The lower dashed line is y = (1/2)x-2

The upper dashed line represents the boundary for y > (1/2)x+3. Region 1 is the set of solution points for y > (1/2)x+3

While the solution set for y < (1/2)x-2 is represented with region 3

There is no overlap between regions 1 and 3 due to the parallel boundary lines.

Put another way: there are no (x,y) points that are in both region 1 and region 3 at the same time.

So that's why there are no solutions to this system of inequalities.

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Alternative method:

Convert the first inequality into Ax+By > C form

y > (1/2)x+3

2y > x + 6 .... multiply both sides by 2

-x+2y > 6 ... subtract x from both sides

z > 6 .... let z = -x+2y

Convert the second inequality into Ax+By < C form

y < (1/2)x-2

2y < x - 4

-x+2y < -4

z < -4 .... let z = -x+2y

We have some number z that is both z > 6 and z < -4 at the same time, but no such number exists. So this is another way to see we have an inconsistent system with no solutions.

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.