|x|+|y|=1+ |xy| how can I graph this?

Question

how can I graph this |x|+|y|=1+ |xy|

Answer 1

All you have to do is determine what the equation will be in each quadrant when the absolute values are removed.

 

To do this, note that |A| = A for all A ≥ 0, and |A| = -A for all A < 0.

 

You should get the following equations for the quadrants.

 

Q1: x + y = 1 + xy

Q2: -x + y = 1 - xy

Q3: -x - y = 1 + xy

Q4: x - y = 1 - xy

 

We can solve each of these for y in terms of x to make graphing easier.

 

Q1,Q2: y = 1

Q3,Q4: y = -1

 

So the graph is just a pair of horizontal lines y = ±1