Question

Indicate whether (2, 7) is a solution of the given system

Answer 1

1st option: Yes, (2, 7) is a solution of the system

Explanation:

We have the following system of inequalities:

`\begin{gathered} y\ge -x+1 \\ \\ y<\:4x+2 \end{gathered}`

We substitute in each inequality the values of x = 2 and y = 7 if the inequality is fulfilled in both cases if it is a solution of the system, otherwise, it would not be a solution.

We check it like this:

`\begin{gathered} 7\ge-2+1\rightarrow7\ge-1\rightarrow\text{ True} \\ \\ 7<\:4\cdot2+2\rightarrow7<8+2\rightarrow7<10\rightarrow\text{ True} \end{gathered}`

Therefore, the correct answer is the 1st option: Yes, (2, 7) is a solution of the system