Question

HELP PLEASEEEE!!!!!!!!

Answer 1

C - with explanation

Explanation:

First, when you graph an inequality that uses a < or > it's plotted with a dashed line to show the line isn't included in the region.

Inequalities with a
`\leq or \geq` are plotted with a solid line to show the line is included in the region.

You can eliminate B and D because they are showing a graph using < or >

Now we know it's either A or C.

To figure out each, let's pick 4 random points, one in each quadrant and color.

Let's pick (3,3) (3, -3) (-3,3) (-3,-3) For an easier visual they would be

|

(-3,3) | (3,3)

___________|____________

|

(-3,-3) | (3,-3)

|

Plus in the values for each inequality:

(3,3) x + 2y
`\leq` 4 3x - y
`\geq` 2

3 +
`\geq` 2(3) 3(3) - 3

3 + 6 = 9 9 - 3 = 6

9 is not
`\leq` to 4 6 is
`\geq` 2

So this is a valid point because it works in the 2nd equation.

We got lucky and the first point we chose eliminates option A because (3,3) is a point that works and option A shows that area as being "out of bounds."

To test option C let's pick a point in the undefined area. Let's choose (-1,3)

(-1,3) x + 2y
`\leq` 4 3x - y
`\geq` 2

-1 +
`\geq` 2(3) 3(-1) - 3

-1 + 6 = 5 -3 - 3 = - 6

5 is not
`\leq` to 4 -6 is not
`\geq` 2

So this point in the white area is not valid for either inequality.

Now we know for sure the correct option is C.

Answer 2

C

Explanation:

We can easily rule out B and D because they have dotted lines and both equations are greater than or equal to and less than or equal to.