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Is $(2,\,8)$ a solution to this system of inequalities? $\newline$ $2x + y \geq 12$ $\newline$ 2x + 2y > 20 $\newline$ 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,\,8)

a solution to this system of inequalities?

\newline

2x + y \geq 12

\newline

2x + 2y > 20

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check First Inequality: Check if $(2, 8)$ satisfies the first inequality $2x + y \geq 12$ . $\newline$ Substitute $x = 2$ and $y = 8$ . $\newline$ $2(2) + 8 \geq 12$ $\newline$ $4 + 8 \geq 12$ $\newline$ $12 \geq 12$ $\newline$ This is true.
Check Second Inequality: Check if $(2, 8)$ satisfies the second inequality 2x + 2y > 20. Substitute $x = 2$ and $y = 8$ . 2(2) + 2(8) > 20 4 + 16 > 20 20 > 20 This is false, it should be 20 > 20, which is not true.

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