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Is $(1,\ 6)$ a solution to this system of inequalities? $\newline$ $y \leq x + 7$ $\newline$ $y \geq 3x + 3$ $\newline$ 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 x + 7

\newline

y \geq 3x + 3

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(1, 6)$ : Does the point $(1, 6)$ satisfy the inequality $y \leq x + 7$ ? $\newline$ Substitute $1$ for $x$ and $6$ for $y$ in $y \leq x + 7$ . $\newline$ $6 \leq 1 + 7$ $\newline$ $6 \leq 8$ $\newline$ Since $6 \leq 8$ is true, $(1, 6)$ satisfies $y \leq x + 7$ .
Substitute in Inequality: Does the point $(1, 6)$ satisfy the inequality $y \geq 3x + 3$ ? $\newline$ Substitute $1$ for $x$ and $6$ for $y$ in $y \geq 3x + 3$ . $\newline$ $6 \geq 3(1) + 3$ $\newline$ $6 \geq 3 + 3$ $\newline$ $6 \geq 6$ $\newline$ Since $6 \geq 6$ is true, $(1, 6)$ satisfies $y \geq 3x + 3$ .
Verify Inequality: Is $(1, 6)$ a solution to the system of inequalities? $\newline$ Since $(1, 6)$ satisfies both inequalities $y \leq x + 7$ and $y \geq 3x + 3$ , it is a solution to the system of inequalities.

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