Answer:
The point does not lie in the solution sets of the given system of inequalities
Step-by-step explanation:
We need to check whether the point (1,-5) is a solution to the system of inequality
[tex]y\le 3x+2[/tex]
[tex]y\:>\:3x+2[/tex]
We substitute x=1 and y=-5 into the top inequality:
[tex]-5\le 3*1+2[/tex]
[tex]-5\le 3+2[/tex]
[tex]-5\le 5[/tex]. This is true
We substitute x=1 and y=-5 into the bottom inequality:
[tex]-5\:>\:-2*1-3[/tex]
[tex]-5\:>\:-2-3[/tex]
[tex]-5\:>\:-5[/tex]. This is false.
Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities.
