Question

Solve the system \(|y| \ge 2\) and \(|x| \le 1\) by graphing.

Please no direct answers :)

Answer 1

hint:
\[\Large |y| \ge 2 \text{ is the same as } -2 \le y \le 2\]

Answer 2

Oh!

Answer 3

Thank you for clarifying that!

Answer 4

oh sorry, I mixed up the signs

I was focusing on x

Answer 5

\[\Large |x| \le 1 \text{ is the same as } -1 \le x \le 1\]

Answer 6

Rule:
\[\Large |x| \le k \text{ is equivalent to } -k \le x \le k\]
where k is any positive number

Answer 7

Ah hah

Answer 8

Rule:
\[\Large |x| \ge k \text{ is equivalent to } x \ge k \text{ or } x \le -k\]
where k is any positive number

Answer 9

they want you to graph it

Answer 10

using that second rule,

\[\Large |y| \ge 2\]

breaks down into

\[\Large y \ge 2 \text{ or } y \le -2\]

Answer 11

So you need to graph the following

\[\Large -2 \le x \le 2, \ y \ge 2, \ y \le -2\]

Answer 12

Okay so the solution is where they intersect/overlap?

Answer 13

correct

Answer 14

Thank you so very much!

Answer 15

looks good so far