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Is $(5,\,6)$ a solution to this system of inequalities? $\newline$ y > 5 $\newline$ 2x + y < 17 $\newline$ 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

(5,\,6)

a solution to this system of inequalities?

\newline

y > 5

\newline

2x + y < 17

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality y > 5: Check if the point $(5, 6)$ satisfies the inequality y > 5. Substitute $6$ for $y$ in y > 5. 6 > 5 Since $6$ is greater than $5$ , the inequality is true.
Check Inequality 2x + y < 17: Check if the point $(5, 6)$ satisfies the inequality 2x + y < 17. $\newline$ Substitute $5$ for $x$ and $6$ for $y$ in 2x + y < 17. $\newline$ 2(5) + 6 < 17 $\newline$ 10 + 6 < 17 $\newline$ $(5, 6)$ $0$ $\newline$ Since $(5, 6)$ $1$ is less than $(5, 6)$ $2$ , the inequality is true.
Determine Solution to System: Determine if $(5, 6)$ is a solution to the system of inequalities. $\newline$ Since $(5, 6)$ satisfies both inequalities y > 5 and 2x + y < 17, it is a solution to the system.

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