Solve the system: the absolute value of y or equal to 2 and the absolute value of x

Question

Solve the system: the absolute value of y >or equal to 2 and the absolute value of x <or equal to 1 by graphing

anonymous · Answer

Have you drawn this yet?

anonymous · Answer

I can't remember how to draw absolute value graphs like that @xartaan

anonymous · Answer

Just to clarify, this is $$|y \ge 2| $$ and $$|x \le 1 |$$ right?

anonymous · Answer

or $$|y| \ge 2   $$ and $$|x| \le 1$$

anonymous · Answer

yep

anonymous · Answer

wait no

anonymous · Answer

the absolute value is just on the x and y

anonymous · Answer

oh wait nvm you got it the second time

anonymous · Answer

A lot of ttimes when graphing things its easier to start with the very basic graph and then adjust it. For example do you know what just the absolute value function looks like?

anonymous · Answer

isn't it like a V shape?

anonymous · Answer

yep. And if you think about it, it makes sense, because if you plug in -1 for x, then |x| is 1. So you get a graph like.

anonymous · Answer

|dw:1378743925989:dw|

anonymous · Answer

The reason I was so confused in none of the graphs for the answer choices is a V shape

anonymous · Answer

Now, if that makes sense to you. Consider the inequality you've got for x. In words "the absolute value of x is less than or equal to 1." Think about what x can be then... |x| immediately tells us that x will be never lower than 0, it can never be negative. Less than or equal to 1, means its will never be bigger than one. If we add those constraints to the picture. We get:

anonymous · Answer

|dw:1378744173279:dw| Just this shaded region.