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Is $(1,\,9)$ a solution to this system of inequalities? $\newline$ $y > x + 5$ $\newline$ $y \geq 5x + 4$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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

Full solution

Q. Is

(1,\,9)

a solution to this system of inequalities?

\newline

y > x + 5

\newline

y \geq 5x + 4

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check First Inequality: Check if $(1, 9)$ satisfies the first inequality $y > x + 5$ . $\newline$ Substitute $x = 1$ and $y = 9$ into the inequality. $\newline$ $9 > 1 + 5$ $\newline$ $9 > 6$ $\newline$ This is true.
Check Second Inequality: Check if $(1, 9)$ satisfies the second inequality $y \geq 5x + 4$ . $\newline$ Substitute $x = 1$ and $y = 9$ into the inequality. $\newline$ $9 \geq 5 \times 1 + 4$ $\newline$ $9 \geq 5 + 4$ $\newline$ $9 \geq 9$ $\newline$ This is also true.
Solution Verification: Since $(1, 9)$ satisfies both inequalities, it is a solution to the system.

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