Answer:
The correct options are:
a. (−2, −14)
b. (3, 5)
Step-by-step explanation:
We are given a linear inequality as follows:
[tex]y-4x\leq -6[/tex]
Now, we are asked to find which ordered pairs are solutions to the given inequality.
i.e. we will check which ordered pair satisfies the given inequality.
a)
(-2,-14)
[tex]-14-4\times (-2)\leq -6\\\\-14+8\leq -6\\\\-6\leq -6[/tex]
The inequality is true.
Hence, option: a is true.
b)
(3,5)
[tex]5-4\times 3\leq -6\\\\5-12\leq -6\\\\-7\leq -6[/tex]
The inequality is true.
Hence, option: b is true.
c)
(-1,-9)
[tex]-9-4\times (-1)\leq -6\\\\-9+4\leq -6\\\\-5\leq -6[/tex]
which is a false identity.
Hence, option: c is incorrect.
d)
(0,-5)
[tex]-5-4\times 0\leq -6\\\\-5\leq -6[/tex]
which is a false identity.
Hence, option: d is incorrect.
e)
(1,3)
[tex]3-4\times 1\leq -6\\\\3-4\leq -6\\\\-1\leq -6[/tex]
which is a false identity.
Hence, option: e is incorrect.
