Answer:
The possible solution to the system of inequalities is:
Option: D
D. (10,1)
Step-by-step explanation:
Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon.
You need to purchase at least 9 gallons of drinks for a neighborhood picnic, but have at most $55 to spend.
This means that the inequalities that will be formed using the above information is:
[tex]x+y\geq 9----------(1)[/tex]
and [tex]4x+6y\leq 55----------(2)[/tex]
Now, we will put the point in the given two inequalities and check which point holds true.
A)
(10,10)
Putting this point in the second inequality we have:
[tex]4\times 10+6\times 10\leq 55\\\\i.e.\\\\40+60\leq 55\\\\i.e.\\\\100\leq 55[/tex]
which is not true.
Hence, Option: A is incorrect.
B)
(10,-5)
Putting this point in first inequality we have:
[tex]10-5\geq 9\\\\i.e.\\\\5\geq 9[/tex]
which is not true.
Hence, option: B is not true.
C)
(2,10)
Putting this point in second inequality we have:
[tex]4\times 2+6\times 10\leq 55\\\\i.e.\\\\8+60\leq 55\\\\i.e.\\\\68\leq 55[/tex]
which is not true.
Hence, Option: C is incorrect.
D)
(10,1)
Putting this point in first inequality we have:
[tex]10+1\geq 9\\\\i.e.\\\\11\geq 9[/tex]
which is true.
Putting this point in second inequality we have:
[tex]4\times 10+6\times 1\leq 55\\\\i.e.\\\\40+6\leq 55\\\\i.e.\\\\46\leq 55[/tex]
which is again true.
Hence, (10,1) is a possible solution to the system of inequalities.
