Solving Coordinate Homework: lxl + lyl = 1

[lovemake1]

Homework Statement

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

Homework Equations

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 ?
please help I am confused.

 

[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?

 

[lovemake1]

hm... logically wouldn't 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

 

[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.

 

[Mark44]

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

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.

 

[lovemake1]

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.

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

 

[Mark44]

OK, that makes more sense. Follow Mentallic's advice in post #2.