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Is $(5,\,5)$ a solution to this system of inequalities? $\newline$ $19x + 13y > 17$ $\newline$ $x + 11y \geq 13$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Is (x, y) a solution to the system of inequalities?

Full solution

Q. Is

(5,\,5)

a solution to this system of inequalities?

\newline

19x + 13y > 17

\newline

x + 11y \geq 13

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(5, 5)$ : Does the point $(5, 5)$ satisfy the inequality $19x + 13y > 17$ ? $\newline$ Substitute $x = 5$ and $y = 5$ into the inequality $19x + 13y > 17$ . $\newline$ $19(5) + 13(5) > 17$ $\newline$ $95 + 65 > 17$ $\newline$ $160 > 17$ $\newline$ The point $(5, 5)$ satisfies the inequality $19x + 13y > 17$ .
Verify Inequality $x + 11y$ : Does the point $(5, 5)$ satisfy the inequality $x + 11y \geq 13$ ? $\newline$ Substitute $x = 5$ and $y = 5$ into the inequality $x + 11y \geq 13$ . $\newline$ $5 + 11(5) \geq 13$ $\newline$ $5 + 55 \geq 13$ $\newline$ $60 \geq 13$ $\newline$ The point $(5, 5)$ satisfies the inequality $x + 11y \geq 13$ .
Solution to System: Is $(5, 5)$ a solution to the system of inequalities? $\newline$ Since $(5, 5)$ satisfies both inequalities $19x + 13y > 17$ and $x + 11y \geq 13$ , it is a solution to the system of inequalities.

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