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Is $(1,\,9)$ a solution to this system of inequalities? $\newline$ y < x + 10 $\newline$ $y \geq 5x + 4$ $\newline$ 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 < x + 10

\newline

y \geq 5x + 4

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(1, 9)$ : Does the point $(1, 9)$ satisfy the inequality: y < x + 10? $\newline$ Substitute $1$ for $x$ and $9$ for $y$ in y < x + 10. $\newline$ 9 < 1 + 10 $\newline$ 9 < 11 $\newline$ Since 9 < 11 is true, $(1, 9)$ satisfies y < x + 10.
Verify Inequality: y < x + 10: Does the point $(1, 9)$ satisfy the inequality: $y \geq 5x + 4$ ? $\newline$ Substitute $1$ for $x$ and $9$ for $y$ in $y \geq 5x + 4$ . $\newline$ $9 \geq 5(1) + 4$ $\newline$ $9 \geq 5 + 4$ $\newline$ $(1, 9)$ $0$ $\newline$ Since $(1, 9)$ $0$ is true, $(1, 9)$ satisfies $y \geq 5x + 4$ .
Verify Inequality: $y \geq 5x + 4$ : Is $(1, 9)$ a solution to the system of inequalities? $\newline$ Since $(1, 9)$ satisfies both y < x + 10 and $y \geq 5x + 4$ , it is a solution to the system of inequalities.

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