Question

Determine if the points are solution points to the inequalities below. If the point is a solution, enter yes. If the point is not a solution, enter no. Enter yes or no in lower case letters (no capital letters). a. Is (2,9) a solution to y<11−x? b. Is (3,9) a solution to y≤15−x? c. Is (4,13) a solution to y>14−x? d. Is (5,9) a solution to y≥15−x?

Answer 1

To determine if the points are solution points to the inequalities which are given:

a) To check (2,9) a solution to y<11−x:

Let us substitute x=2 and y=9, we get

`\begin{gathered} 9<11-2 \\ 9<9 \end{gathered}`

The answer is, No, (2,9) is not a solution to y<11−x.

b) To check (3,9) a solution to y≤15−x:

Put x=3 and y=9 we get,

`\begin{gathered} 9\leq15-3 \\ 9\leq12 \end{gathered}`

Since, 9 less than 12.

Hence, the answer is, yes (3,9) is a solution to y≤15−x.

c) To check (4,13) a solution to y>14−x:

Put x=4 and y=13 we get,

`\begin{gathered} 13>14-4 \\ 13>10 \end{gathered}`

Hence, the answer is yes, (4,13) is a solution to y>14−x.

d) To check (5,9) a solution to y≥15−x:

Put x=5 and y=9 we get,

`\begin{gathered} 9\ge15-5 \\ 9\ge10 \end{gathered}`

Since, 9 is not greater than 10.

Hence, the answer is No, (5,9) is not a solution to y≥15−x.