Answer:
Part 1) The solution set is (-15,∞) ∩ (-∞,9)=(-15,9)
Part 2) The ordered pair (1,3) is a solution of the system
Step-by-step explanation:
Part 1) we have
![\left|x+3\right|](https://tex.z-dn.net/?f=%5Cleft%7Cx%2B3%5Cright%7C%3C12)
<u>First solution case Positive</u>
![+(x+3)](https://tex.z-dn.net/?f=%2B%28x%2B3%29%3C12)
![x](https://tex.z-dn.net/?f=x%3C12-3)
![x](https://tex.z-dn.net/?f=x%3C9)
The solution first case is the interval -------> (-∞,9)
<u>Second solution case Negative</u>
![-(x+3)](https://tex.z-dn.net/?f=-%28x%2B3%29%3C12)
![-x-3](https://tex.z-dn.net/?f=-x-3%3C12)
![-x](https://tex.z-dn.net/?f=-x%3C12%2B3)
------> Multiply by -1 both sides
![x>-15](https://tex.z-dn.net/?f=x%3E-15)
The solution second case is the interval -------> (-15,∞)
The solution set is equal to
(-15,∞) ∩ (-∞,9)=(-15,9)
Part 2) we have
-------> inequality A
-----> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
Verify each case
case a) (1,5)
Substitute the value of x and the value of y in the inequality and then compare
<u>Inequality A</u>
------> is true
<u>Inequality B</u>
![1+5\leq 4](https://tex.z-dn.net/?f=1%2B5%5Cleq%204)
-----> is not true
therefore
the ordered pair is not a solution
case b) (0,5)
Substitute the value of x and the value of y in the inequality and then compare
<u>Inequality A</u>
------> is true
<u>Inequality B</u>
![0+5\leq 4](https://tex.z-dn.net/?f=0%2B5%5Cleq%204)
-----> is not true
therefore
the ordered pair is not a solution
case c) (-2,-3)
Substitute the value of x and the value of y in the inequality and then compare
<u>Inequality A</u>
------> is not true
therefore
the ordered pair is not a solution
case d) (1,3)
Substitute the value of x and the value of y in the inequality and then compare
<u>Inequality A</u>
------> is true
<u>Inequality B</u>
![1+3\leq 4](https://tex.z-dn.net/?f=1%2B3%5Cleq%204)
-----> is true
therefore
the ordered pair is a solution