Answer:
c) (-16,3)
Step-by-step explanation:
Given: inequality [tex]12+\text{y}\leq -3\text{x}[/tex]
To Find: Which ordered pair is part of the solution set of the inequality
Solution:
Simplifying inequality,
[tex]12+\text{y}\leq -3\text{x}[/tex]
[tex]12}\leq -3\text{x}-\text{y[/tex]
now,
putting ordered pairs from options
a) [tex](3,-16)[/tex]
[tex]-3\times3-(-16)[/tex][tex]16-9=7[/tex]
as [tex]7<12[/tex], it does not satisfy inequality
b) [tex](4,-1)[/tex]
[tex]-3\times4-(-1)[/tex][tex]1-12=-11[/tex]
as [tex]-11<12[/tex], it does not satisfy inequality
c) [tex](-16,3)[/tex]
[tex]-3\times(-16)-(3)[/tex][tex]48-3=45[/tex]
as [tex]45>12[/tex], it satisfy inequality
d) [tex](1,4)[/tex]
[tex]-3\times1-(4)[/tex][tex]-3-4=-7[/tex]
as [tex]-7<12[/tex], it does not satisfy inequality
So, from above only option c is part of the solution set of inequality.
