Question

Determine which point is NOT a solution to the system of inequalities by graphing.

y < 3x + 3

x + 4y > 4
Choose one answer.
a. (0,2)
b. (2,2)
c. (3,0)
d. (4,1)

Answer 1

Choose an answer that makes sense with inputting the y and x in the ordered pair in both equations

Answer 2

First, you have to solve for y; get y alone for both equations (one is already done for you). Remember, if you divide by a negative number, the sign changes.
From then, you plug in each individual x-value for both equations, and upon getting the y-value, read it out (I will plug In the x-value for a [which is 0]):
\[y<3x+3 \rightarrow y<3(0)+3\rightarrow y<3\]
The original point they gave was (0,2). When you read out what we got, "y is less than 3", the value "2" would satisfy that statement; we can substitute the number "2" for y, and get "2 is less than 3". Which is true.
Now for the other one:
\[x+4y>4\rightarrow 4y>4-x \rightarrow y>1-(x/4)\]
Plug in the chosen x-value:
\[y>1-(x/4)\rightarrow y>1-(0/4)\rightarrow y>1-0\rightarrow y>1\]
Now we read and substitute out: "y is greater than 1" [the point that we chose was (0,2)]; "2 is greater than 1". This is also true.
Therefore, this is not the answer because the question is asking which IS FALSE. Meaning, when you do the last step, you will get a false statement; example : "5 is greater than 6".
When you see a false statement as such, that is your answer.
I hope this helped, feel free to pst if you need further elaboration, or assistance with any other problem.
P.S. To save you time, try the point (4,1) ;)