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Is $(9,\,1)$ a solution to this system of inequalities? $\newline$ $x + y \leq 10$ $\newline$ $y \geq 5$ $\newline$ 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,\,1)

a solution to this system of inequalities?

\newline

x + y \leq 10

\newline

y \geq 5

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality Satisfaction: Does the point $(9, 1)$ satisfy the inequality $x + y \leq 10$ ? $\newline$ Substitute $9$ for $x$ and $1$ for $y$ in $x + y \leq 10$ . $\newline$ $9 + 1 \leq 10$ $\newline$ $10 \leq 10$ $\newline$ Since $10 \leq 10$ is true, $(9, 1)$ satisfies $x + y \leq 10$ .
Substitute Values: Does the point $(9, 1)$ satisfy the inequality $y \geq 5$ ? $\newline$ Substitute $1$ for $y$ in $y \geq 5$ . $\newline$ $1 \geq 5$ $\newline$ Since $1 \geq 5$ is false, $(9, 1)$ does not satisfy $y \geq 5$ .
Verify Inequality Result: Is $(9, 1)$ a solution to the system of inequalities? $\newline$ Since $(9, 1)$ does not satisfy both inequalities, it is not a solution to the system of inequalities.

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