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Is $(2,\,1)$ a solution to this system of inequalities? $\newline$ $x + 8y \geq 6$ $\newline$ $y \leq 8$ $\newline$ 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

(2,\,1)

a solution to this system of inequalities?

\newline

x + 8y \geq 6

\newline

y \leq 8

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality Satisfaction: Does the point $(2, 1)$ satisfy the inequality $x + 8y \geq 6$ ? $\newline$ Substitute $2$ for $x$ and $1$ for $y$ in $x + 8y \geq 6$ . $\newline$ $2 + 8(1) \geq 6$ $\newline$ $2 + 8 \geq 6$ $\newline$ $10 \geq 6$ $\newline$ Since $10 \geq 6$ is true, $(2, 1)$ satisfies $x + 8y \geq 6$ .
Substitute Values: Does the point $(2, 1)$ satisfy the inequality $y \leq 8$ ? $\newline$ Substitute $1$ for $y$ in $y \leq 8$ . $\newline$ $1 \leq 8$ $\newline$ Since $1 \leq 8$ is true, $(2, 1)$ satisfies $y \leq 8$ .
Verify Inequality Satisfaction: Is $(2, 1)$ a solution to the system of inequalities? $\newline$ Since $(2, 1)$ satisfies both inequalities $x + 8y \geq 6$ and $y \leq 8$ , it is a solution to the system of inequalities.

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