Question 227119: Solve the system |y|>/= 2 |x|
I think it might be no solution, but I'm not sure. Can someone please help?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Not sure what your equation is.
|y| >= 2 has a solution.
The solution is y >= 2 or y <= -2
|x| <= 1 also has a solution.
The solution is -1 <= x <= 1
|y| >= 2*|x| also has a solution.
The solution is y >= 2*|x| or y <= -2*|x|
I could go further but it would get more complicated and you might not need to do so.
In order to test the solutions out, you need to put in test cases where the value of y is within limits and the value of y is out of limits to see if the equations hold true or not.
Let's take |y| >= 2
Let y = -3, -2, 0, 1, 2, 3
We get |y| equal to 3, 2, 0, 1, 2, 3
|y| >= 2 when y = -3, -2, 2, 3 which is consistent with our requirements that y >= 2 or y <= -2.
Let's take |x| <= 1
Let x = -2, -1, 0, 1, 2
Then |x| = 2, 1, 0, 1, 2
|x| <= 1 when x = -1, 0, 1 which is consistent with our requirements that -1 <= x <= 1
Let's take |y| >= 2*|x|
Let |x| = 5
This means that 2*|x| = 10
Let's take y = -15, -10, 0, 10, 15
Then |y| = 15, 10, 0, 10, 15
|y| >= 10 when y = -15, -10, 10, 15 which is consistent with out requirements that y <= -10 or y >= 10
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