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Is $(1,\,9)$ a solution to this system of inequalities? $\newline$ y > 5 $\newline$ $y \leq x + 6$ $\newline$ 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

(1,\,9)

a solution to this system of inequalities?

\newline

y > 5

\newline

y \leq x + 6

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality: Does the point $(1, 9)$ satisfy the inequality y > 5? $\newline$ Substitute $1$ for $x$ and $9$ for $y$ in y > 5. $\newline$ 9 > 5 $\newline$ Since 9 > 5 is true, $(1, 9)$ satisfies y > 5.
Substitute Values: Does the point $(1, 9)$ satisfy the inequality $y \leq x + 6$ ? $\newline$ Substitute $1$ for $x$ and $9$ for $y$ in $y \leq x + 6$ . $\newline$ $9 \leq 1 + 6$ $\newline$ $9 \leq 7$ $\newline$ Since $9 \leq 7$ is false, $(1, 9)$ does not satisfy $y \leq x + 6$ .
Evaluate Inequality: Is $(1, 9)$ a solution to the system of inequalities? $\newline$ Since $(1, 9)$ satisfies the first inequality y > 5 but does not satisfy the second inequality $y \leq x + 6$ , $(1, 9)$ is not a solution to the system of inequalities.

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