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Is $(4,\,6)$ a solution to this system of inequalities? $\newline$ 19x + 9y > 14 $\newline$ $x + y \leq 10$ $\newline$ 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

(4,\,6)

a solution to this system of inequalities?

\newline

19x + 9y > 14

\newline

x + y \leq 10

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(4, 6)$ : Let's first check if the point $(4, 6)$ satisfies the inequality 19x + 9y > 14. Substitute $4$ for $x$ and $6$ for $y$ in 19x + 9y > 14. 19(4) + 9(6) > 14 76 + 54 > 14 $(4, 6)$ $0$ Since $(4, 6)$ $0$ is true, $(4, 6)$ satisfies the first inequality.
Substitute Values: Now let's check if the point $(4, 6)$ satisfies the inequality $x + y \leq 10$ . $\newline$ Substitute $4$ for $x$ and $6$ for $y$ in $x + y \leq 10$ . $\newline$ $4 + 6 \leq 10$ $\newline$ $10 \leq 10$ $\newline$ Since $10 \leq 10$ is true, $(4, 6)$ satisfies the second inequality.
Verify First Inequality: Since the point $(4, 6)$ satisfies both inequalities in the system, it is a solution to the system of inequalities.

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