Question

Which graph represents the system of inequalities?

y- 2x < -3

y-4 < -2x

y >-1/4x

Answer 1

We can start with y-2x<3. Graphing it out (y-2x=3), we can see that it can be one of two sides. To graph y-2x=3, we can add 2x to both sides to get 2x+3=y and plug a x value in, then get a y value as an output. Connect the dots (the points) and you should have your line!)  Since one side has, for example, (5,0) we can plug that in to get 0-(-10)=10 which is not less than 3. Therefore, it is on the other side, so you can shade that in. Repeat the process for the other two inequalities, and see where all 3 overlap to get your answer, which would end up to be the top right one

Answer 2

A

Step-by-step explanation:

Let's do it step by step, literally.

1)For that system, let's start with the first inequality by graphing it:

`y-2x<3`

Since it is lesser than the 2nd member, i.e. -3 it is graphed by a dashed line then the shaded part is to the right

(Check the 1st picture)

2) Similarly, for the 2nd inequality graph it with a dashed line to the right. And the shaded region to the right.

`y-4<-2x`

The second picture shows the overlapping of both.

(2nd picture below)

3) Finally, the last inequality is a dashed line passing through the origin whose slope is negative, and the darker region is a little triangle.

`y>-(1)/(4)x`