Homework Help: Finding co-ordinate

1. Sep 22, 2010

lovemake1

1. The problem statement, all variables and given/known data

find the set of all points (x,y) which satisfy lxl + lyl = 1

2. Relevant equations

3. The attempt at a solution

first i decided to make lxl and lyl into inequality.

-1 < x < 1
-1 < y < 1

lxl = lyl - 1

so from any value of y between (-1,1) would work ? will this give lxl the correct result?
will they both equal to 1 ?

2. Sep 23, 2010

Mentallic

There are 4 cases to consider:

x,y>0
x>0, y<0
x<0, y>0
x,y<0

For the first, obviously you have the line y=1-x. And yes you place the restrictions that $0\leq x\leq 1$. Can you finish the rest?

3. Sep 23, 2010

lovemake1

hm... logically wouldnt y = 1 - x be the only solution ? since we are not dealing with absolute values anymore.

or should i keep absolute values in the calculations?

lyl = 1 - lxl

-1 < x < 0

4. Sep 23, 2010

Mentallic

Well that's like saying logically shouldn't x=1 be the only solution to |x|=1.

The point (-1/2, 1/2) satisfies the equation, but this point doesn't lie on the line y=1-x. Try do what I suggested in my previous post.

5. Sep 23, 2010

Staff: Mentor

Is this exactly how the problem is stated?

A reasonable, but not very helpful, answer is {(x, y) | |x| + |y| = 1}. Another reasonable answer is a graph of this equation.

6. Sep 24, 2010

lovemake1

The question asks to graph for all coordinates (x,y) which satisfy l x l + l y l = 1

7. Sep 24, 2010