Question

HELP PLEASEEEE!!!!!!!!

Answer 1

Answer:

C - with explanation

Step-by-step 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

Answer:

C

Step-by-step 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.