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Is $(2,\,1)$ a solution to this system of inequalities? $\newline$ $2x + 13y \leq 17$ $\newline$ x + 11y > 13 $\newline$ 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

(2,\,1)

a solution to this system of inequalities?

\newline

2x + 13y \leq 17

\newline

x + 11y > 13

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality Satisfaction: Does the point $(2, 1)$ satisfy the inequality $2x + 13y \leq 17$ ? $\newline$ Substitute $2$ for $x$ and $1$ for $y$ in $2x + 13y \leq 17$ . $\newline$ $2(2) + 13(1) \leq 17$ $\newline$ $4 + 13 \leq 17$ $\newline$ $17 \leq 17$ $\newline$ Since $17 \leq 17$ is true, $(2, 1)$ satisfies the inequality $2x + 13y \leq 17$ .
Substitute Values: Does the point $(2, 1)$ satisfy the inequality x + 11y > 13? $\newline$ Substitute $2$ for $x$ and $1$ for $y$ in x + 11y > 13. $\newline$ 2 + 11(1) > 13 $\newline$ 2 + 11 > 13 $\newline$ 13 > 13 $\newline$ Since 13 > 13 is false (it should be x + 11y > 13 $1$ ), $(2, 1)$ does not satisfy the inequality x + 11y > 13.

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