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Is $(1,\,9)$ a solution to this system of inequalities? $\newline$ $y > 5x + 2$ $\newline$ $y < x + 10$ $\newline$ 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 > 5x + 2

\newline

y < x + 10

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point Satisfaction: Does the point $(1, 9)$ satisfy the inequality $y > 5x + 2$ ? $\newline$ Substitute $x = 1$ and $y = 9$ into the inequality $y > 5x + 2$ . $\newline$ $9 > 5(1) + 2$ $\newline$ $9 > 5 + 2$ $\newline$ $9 > 7$ $\newline$ The point $(1, 9)$ satisfies the inequality $y > 5x + 2$ .
Verify Inequality: Does the point $(1, 9)$ satisfy the inequality $y < x + 10$ ? $\newline$ Substitute $x = 1$ and $y = 9$ into the inequality $y < x + 10$ . $\newline$ $9 < 1 + 10$ $\newline$ $9 < 11$ $\newline$ The point $(1, 9)$ satisfies the inequality $y < x + 10$ .
Solution to System: Is $(1, 9)$ a solution to the system of inequalities? $\newline$ Since the point $(1, 9)$ satisfies both inequalities $y > 5x + 2$ and $y < x + 10$ , it is a solution to the system of inequalities.

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