# How do you find the solution to #x - y > 3# and #x + y < 3#?

##### 1 Answer

A solution to a system of two inequalities with two variables

If you are looking for a solution to these two inequalities in terms of two separate inequalities, one for

The best approach to "solve" this system of two inequalities is to better represent all the pairs

Let's represent the solutions to this system of inequalities (that is, all pairs

First of all, let's transform both inequalities in a more graph-friendly representation.

Add the same number

Add the same number

Now we have two inequalities:

Let's graph them now.

The graph of

graph{x-3 [-6, 6, -4, 2]}

All pairs

All pairs

All pairs

So, all the solutions to the first inequality are those pairs

Similarly, the graph of

graph{-x+3 [-6, 6, -4, 2]}

All pairs

All pairs

All pairs

So, all the solutions to the second inequality are those pairs

Notice that both graphs intersect at a point

Now we have to imagine an area on the coordinate plane that is **both below the first graph AND below the second graph**. This area represents a solution to a system of two inequalities we have.

You can consider this area as a quarter of a plain with a vertex at a point

Here is a graphical representation of this area with solutions to our system of inequalities being all the pairs

graph{-|x-3| [-6, 6, -3, 3]}

Incidentally, you can express this with another inequality: