A system of linear inequalities is shown below:

y -2x -2 y + 0
Describe the steps to graph the solution set to the system of inequalities.

Question

A system of linear inequalities is shown below:

 y > -2x -2 y + >0
Describe the steps to graph the solution set to the system of inequalities.

anonymous · Answer

@m&msdoodle Is it ok if u could help me?

anonymous · Answer

Im not really good with graphs, sorry!

anonymous · Answer

It's ok thx :) anyways though :D

akashdeepdeb · Answer

Can you write the equations again? It does not look right.

anonymous · Answer

|dw:1403790757440:dw|

Is this any better ?

akashdeepdeb · Answer

Yes, much better. :D

As this is an inequality, it is going to cover some area on the cartesian plane!
That means, it is not a specific point that satisfy the inequality but a bunch of points which do. :)

We can get 2 equations, which are:

1) $~~y \ge -2x - 2~~~~$ or $~~~~y \le 2x + 2$ [The inequality switches when multiplied with -1]
2) $~~y+x \ge 0$

Okay, so, now the obvious question is, how do we plot the graph?

We we can do this one thing.

Let us say we had the lines (equations) , WITHOUT the inequality,
We'd have then, 

1) $~~y = 2x + 2$
2) $~~x+y = 0$

Now plot these lines on a graph.

It looks like something like this: 

|dw:1403791221003:dw|

Now, take a random point, NOT on the line, and see if they satisfy the inequalities.

Are you getting this till here?
This is a step-by-step process.

anonymous · Answer

yea sorry my laptop had gotten over heated so it had shut off on me so i had jumped on my desktop, but i understand what you saying

akashdeepdeb · Answer

One sec...

anonymous · Answer

ok :)

akashdeepdeb · Answer

Are you getting this?

anonymous · Answer

yea

akashdeepdeb · Answer

Try doing the same with the second equation. 
If the point you take, does not satisfy the inequality then ALL the points on the other side of the line, must!
After covering the whole area for both the inequalities. The INTERSECTION of the areas shows you the solution set for the graph. :)

anonymous · Answer

ok so will i need to use (1,0) for this one?

akashdeepdeb · Answer

You can use any point. Try to use a point which does not lie on the point.
And if the point satisfies the inequality then check which side of the line it lies on.
If the point you choose does not satisfy the inequality then choose the other side of the line as they will contain all the points in the solution set.
:)