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Is $(1,\,2)$ a solution to this system of inequalities? $\newline$ $2x + 9y \leq 20$ $\newline$ 13x + y < 16 $\newline$ 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,\,2)

a solution to this system of inequalities?

\newline

2x + 9y \leq 20

\newline

13x + y < 16

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(1, 2)$ : Does the point $(1, 2)$ satisfy the inequality $2x + 9y \leq 20$ ? $\newline$ Substitute $1$ for $x$ and $2$ for $y$ in $2x + 9y \leq 20$ . $\newline$ $2(1) + 9(2) \leq 20$ $\newline$ $2 + 18 \leq 20$ $\newline$ $(1, 2)$ $0$ $\newline$ Since $(1, 2)$ $0$ is true, $(1, 2)$ satisfies the inequality $2x + 9y \leq 20$ .
Check Point $(1, 2)$ : Does the point $(1, 2)$ satisfy the inequality 13x + y < 16? $\newline$ Substitute $1$ for $x$ and $2$ for $y$ in 13x + y < 16. $\newline$ 13(1) + 2 < 16 $\newline$ 13 + 2 < 16 $\newline$ $(1, 2)$ $0$ $\newline$ Since $(1, 2)$ $0$ is true, $(1, 2)$ satisfies the inequality 13x + y < 16.
Solution Verification: Is $(1, 2)$ a solution to the system of inequalities? $\newline$ Since $(1, 2)$ satisfies both inequalities $2x + 9y \leq 20$ and 13x + y < 16, it is a solution to the system of inequalities.

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