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Is $(9,\,3)$ a solution to this system of inequalities? $\newline$ $x \geq 6$ $\newline$ $x + y \leq 12$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Is (x, y) a solution to the system of linear inequalities?

Full solution

Q. Is

(9,\,3)

a solution to this system of inequalities?

\newline

x \geq 6

\newline

x + y \leq 12

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $9, 3$ : Does the point $9, 3$ satisfy the inequality $x \geq 6$ ? $\newline$ Substitute $9$ for $x$ in $x \geq 6$ . $\newline$ $9 \geq 6$ $\newline$ Since $9$ is greater than $6$ , $9, 3$ satisfies the inequality $x \geq 6$ .
Substitute Values: Does the point $(9, 3)$ satisfy the inequality $x + y \leq 12$ ? $\newline$ Substitute $9$ for $x$ and $3$ for $y$ in $x + y \leq 12$ . $\newline$ $9 + 3 \leq 12$ $\newline$ $12 \leq 12$ $\newline$ Since $12$ is equal to $12$ , $(9, 3)$ satisfies the inequality $x + y \leq 12$ .
Verify Solutions: Is $(9, 3)$ a solution to the system of inequalities? $\newline$ Since $(9, 3)$ satisfies both inequalities $x \geq 6$ and $x + y \leq 12$ , it is a solution to the system of inequalities.

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