Question

The coordinate grid shows points a through k. Which points are solutions to the system of inequalities 2x+y 8 please help this is my last resort

Answer 1

The points that verify the system of inequalities are:

point E, pointF, and point G.

Explanation:

Please see the attached image that illustrates the boundary lines in your system of inequalities.

The boundary line for the inequality
`2x+y<10` is depicted in green, while the boundary line for the inequality
`2x-4y>8` is depicted in red.

By solving for y in each inequality, we understand which half-plane should be considered for the inequality:

First inequality (green boundary line) :

`2x+y<10\\y=10-2x`

This means that we are to consider the points below the green boundary line.

Second inequality (red boundary line) :

`2x-4y >8\\2x-8>4y\\y<(1)/(2) x-2`

This means we have to consider the points below the red boundary line.

Recall as well that both conditions we arrived at have to be satisfied by the points that are solutions of both inequalities.

From the image, we can see that there are only three points that reside at the same time below the green and the red boundary lines. These points are: point E, pointF, and point G.

On the other hand, we have two points that lie on a boundary line (point J and H), but they should be ignored, since the system of inequalities contain just inequality symbols < or >, and not the "equal" sign.