Respuesta :

Answer:

  • If x= 16 then y= -16
  • and if x= -16 then y= 16

Step-by-step explanation:

It is given that:

   |x|=16

i.e. x= 16 or x= -16

and   |y|=16

i.e.  y=16  or   y= -16

Also, the values of x and y are such that when they are combined then it is equal to 0.

so, if x= 16 and y= -16

Then we have:

x+y=16-16=0

Also,

if x= -16 and y=16 then we have:

  x+y = -16+16=0

Using the absolute value concept, the options are:

  • x = 16 and y = -16.
  • x = -16 and y = 16.

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Absolute value:

[tex]|x| = a[/tex] means that: [tex]x = a[/tex], or [tex]x = -a[/tex]

Thus:

  • [tex]|x| = 16 \rightarrow x = 16[/tex] or [tex]x = -16[/tex]
  • [tex]|y| = 16 \rightarrow y = 16[/tex] or [tex]y = -16[/tex]

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The possible combinations are:

  • [tex]x = 16, y = 16, x + y = 16 + 16 = 32[/tex]
  • [tex]x = 16, y = -16, x + y = 16 - 16 = 0[/tex]
  • [tex]x = -16, y = 16, x + y = -16 + 16 = 0[/tex]
  • [tex]x = -16, y = -16, x + y = -16 - 16 = -32[/tex]

Thus, two combinations achieve the desired result:

  • x = 16 and y = -16.
  • x = -16 and y = 16.

A similar problem is given at https://brainly.com/question/15207259