|x| + |y| = 4

• Jun 27th 2011, 04:13 AM
ejaykasai
|x| + |y| = 4
sir what if the question is like this?

|x|+|y|=4 ?
• Jun 27th 2011, 04:46 AM
mr fantastic
Re: |x| + |y| = 4
Quote:

Originally Posted by ejaykasai
sir what if the question is like this?

|x|+|y|=4 ?

The graph is here: plot &#124;x&#124; &#43; &#124;y&#124; &#61; 4 - Wolfram|Alpha

Knowing the answer, and understanding what |x| and |y| mean, you should be able to figure out where the answer comes from.
• Jun 27th 2011, 10:23 AM
HallsofIvy
Re: |x| + |y| = 4
Quote:

Originally Posted by ejaykasai
sir what if the question is like this?

|x|+|y|=4 ?

That's not a question- it is an equation. What do you want to do with it?
If, as mr fantastic suggests, you want to graph it then do what is standard for absolute value: look at positive and negative values.

If both x and y are non-negative, |x|= x, |y|= y so the equation becomes x+ y= 4. If x= 0, y= 4 and if y= 0, x= 4. That is a straight line, in the first quadrant, with endpoints (0, 4) and (4, 0). If x is negative, but y is positive, |x|= -x, |y|= y so the equation becomes -x+ y= 4 or y= x+ 4. When x= 0, y= 4. When y= 0, x= -4. That is a straight line, in the second quadrant, with endpoints (0, 4), (-4, 0). If both x and y are negative, |x|= -x, |y|= -y so the equation becomes -x- y= 4. If x= 0, y= -4 and if y= 0, x= -4. That is a straight line, in the third quadrant, with endpoints (0, -4) and (-4, 0). Finally, if x> 0, y< 0, |x|= x, |y|= -y and the equation becomes x- y= 4 or y= x- 4. If x= 0, y= -4. If y= 0, x= 4. Thatis a straight line, in the fourth quadrant, with endpoints (0, -4), (4, 0).

Putting those all together, the graph is a square with diagonals along the x and y axes with vertices (4, 0), (0, 4), (-4, 0), (0, -4).