The solution to the system x + y > 9 and x + y > 7 is the shaded region which lies:?

Question

a. between the lines x + y = 9 and x + y = 7.

b. above the line y = 9 – x and below the line x = 7 – y.

c. above the line x + y = 9.

d. below the line x + y = 7.

AND:

Which point satisfies the system of inequalities: x – 3y > 5 and 2x + y < 2?

a. (–2, 3)

b. (5, 1)

c. (12, 20)

d. (1, –5)

Answer 1

above line x+y=9
and above the line x + y = 7
thus netto above the line x + y = 9

AND

just fill in the x and y : d

Answer 2

The region of the graph shaded by the inequation x+y>9 is the region above this line.

I think you know how to plot this line. This line has a negative slope.

In the same way the region of the graph shaded by the inequation x+y>7 is also the region above this line only.

So to get the common answer, you should look for the common region and that will be the solution. In this case the solution of the two inequations is the region above the line x+y=9.

The answer is c as per your options.

2. The second part can be done in two ways. The first way is so simple that you have to substitute the value given and see that the inequation is satis fied in both the inequations. then that will be your point that satisfies the given inequations.

For easier understanding, I am checking the first option (-2,3)
Substitute in first equation, -2 -3(3) > 5 does not satisfy so the option a is not the answer. Similarly do for the remaining options and you will get the fourth option as the answer.

The second method is very lengthy and it is not advisable to explain.

Hope you understand this answer.

Answer 3

Okay. In order to do this, you first need to change the equations to have y on the left by itself.

x + y > 9
y > -x + 9

x + y > 7
y > -x + 7

Okay, since both of the equations are (y >), you know that the shading will be ABOVE them, where y gets larger. You can then use process of elimination to find your solution.

Answer A cannot be right, because between means below one and above the other. You need above BOTH.

Answer B cannot be right, because you need above BOTH, not below one.

Answer C COULD be right because it is saying ABOVE one of the lines. You do not know for sure because it does not mention the other line.

Answer D cannot be right, because it is saying below a line, and you need ABOVE both lines.

Your answer is C!

Next.

There are a few ways of doing this one. I know one way that cannot be shown on here. (1) Graph it and look for the answer choices on the graph. Pick the one that is in the shaded region.

Answer 4

the answer to the first question is c, above the line x + y>9, since the "and" connector means the points must satisfy both inequalities at the same time.

the answers to the second question are a and d. Substitution will show you that the point in a makes both true, and the point in d makes both true.

Answer 5

The shaded area is the rejection area of H subzero in your hypothesis...oh wait....wrong answer huh?

Answer 6

gimb got spot on

Answer 7

I agree with gimb. Thanks for the easy 2 points. Have a good day.