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Is $(1,\,6)$ a solution to this system of inequalities? $\newline$ $y \leq 7$ $\newline$ 2x + y < 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

(1,\,6)

a solution to this system of inequalities?

\newline

y \leq 7

\newline

2x + y < 8

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality: Does the point $(1, 6)$ satisfy the inequality $y \leq 7$ ? $\newline$ Substitute $6$ for $y$ in $y \leq 7$ . $\newline$ $6 \leq 7$ $\newline$ Since $6 \leq 7$ is true, $(1, 6)$ satisfies $y \leq 7$ .
Substitute Values: Does the point $(1, 6)$ satisfy the inequality 2x + y < 8? $\newline$ Substitute $1$ for $x$ and $6$ for $y$ in 2x + y < 8. $\newline$ 2(1) + 6 < 8 $\newline$ 2 + 6 < 8 $\newline$ 8 < 8 $\newline$ Since 8 < 8 is false (it should be 2x + y < 8 $1$ ), $(1, 6)$ does not satisfy 2x + y < 8.

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