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Is $(1,\ 1)$ a solution to this system of inequalities? $\newline$ $12x + 4y \leq 20$ $\newline$ $8x + y \geq 12$ $\newline$ 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

(1,\ 1)

a solution to this system of inequalities?

\newline

12x + 4y \leq 20

\newline

8x + y \geq 12

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality $1$ : Check if $(1, 1)$ satisfies the inequality $12x + 4y \leq 20$ . Substitute $x = 1$ and $y = 1$ into the inequality. $12(1) + 4(1) \leq 20$ $12 + 4 \leq 20$ $16 \leq 20$ , which is true.
Check Inequality $2$ : Check if $(1, 1)$ satisfies the inequality $8x + y \geq 12$ . Substitute $x = 1$ and $y = 1$ into the inequality. $8(1) + 1 \geq 12$ $8 + 1 \geq 12$ $9 \geq 12$ , which is false.

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