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Is $(1,\,7)$ a solution to this system of inequalities? $\newline$ $y \leq x + 6$ $\newline$ $y \geq 4x + 3$ $\newline$ 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,\,7)

a solution to this system of inequalities?

\newline

y \leq x + 6

\newline

y \geq 4x + 3

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality $1$ : Check if $(1, 7)$ satisfies the inequality $y \leq x + 6$ . $\newline$ Substitute $x = 1$ and $y = 7$ . $\newline$ $7 \leq 1 + 6$ $\newline$ $7 \leq 7$ $\newline$ This is true.
Check Inequality $2$ : Check if $(1, 7)$ satisfies the inequality $y \geq 4x + 3$ . $\newline$ Substitute $x = 1$ and $y = 7$ . $\newline$ $7 \geq 4(1) + 3$ $\newline$ $7 \geq 4 + 3$ $\newline$ $7 \geq 7$ $\newline$ This is also true.
Solution Verification: Since $(1, 7)$ satisfies both inequalities, it is a solution to the system.

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