Question

What values do x and y have if |x| =16 and |y| =16, and when x and y are combined they equal 0

Answer 1

x = 16, y = -16

or

x = -16, y = 16

Explanation:

|x| =16 ---> x = -16 or x = 16

|y| =16 ---> y = -16 or y = 16

it is given that x + y =0,

If x = -16, then

-16 + y = 0 or y = 16

hence x = -16 and y = 16 is one possible combination for the values of x and y

If x = 16, then

16 + y = 0 or y = -16

hence x = 16 and y = -16 is another possible combination for the values of x and y

Answer 2

`x=-16\,,\,y=16\,\,or\,\,x=16\,,\,y=-16`

Explanation:

Given:
`\left | x \right |=16\,,\,\left | y \right |=16`

To find: values of x and y such that when they are combined, we get 0.

Solution:

We know that for
`\left | x \right |=y`, we have
`x=\pm y`

`\left | x \right |=16\Rightarrow x=\pm 16` as
`\left | 16 \right |=16\,,\,\left | -16 \right |=16`

`\left | y \right |=16\Rightarrow y=\pm 16` as
`\left | 16 \right |=16\,,\,\left | -16 \right |=16`

Case 1:

Take
`x=16\,,\,y=-16`

`x+y=16+(-16)=16-16=0`

Case 2:

`x=-16\,,\,y=16`

`x+y=\left ( -16 \right )+16=-16+16=0`

Therefore, for
`x=-16\,,\,y=16\,\,or\,\,x=16\,,\,y=-16`, combined value of x and y is 0.