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Is $(3,\ 8)$ a solution to this system of inequalities? $\newline$ y < 6x + 4 $\newline$ y < x + 6 $\newline$ 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

(3,\ 8)

a solution to this system of inequalities?

\newline

y < 6x + 4

\newline

y < x + 6

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(3, 8)$ : Does the point $(3, 8)$ satisfy the inequality y < 6x + 4? $\newline$ Substitute $3$ for $x$ and $8$ for $y$ in y < 6x + 4. $\newline$ 8 < 6(3) + 4 $\newline$ 8 < 18 + 4 $\newline$ $(3, 8)$ $0$ $\newline$ Since $(3, 8)$ $0$ is true, $(3, 8)$ satisfies y < 6x + 4.
Substitute Values: Does the point $(3, 8)$ satisfy the inequality y < x + 6? $\newline$ Substitute $3$ for $x$ and $8$ for $y$ in y < x + 6. $\newline$ 8 < 3 + 6 $\newline$ 8 < 9 $\newline$ Since 8 < 9 is true, $(3, 8)$ satisfies y < x + 6.
Verify Solutions: Is $(3, 8)$ a solution to the system of inequalities? $\newline$ Since $(3, 8)$ satisfies both inequalities y < 6x + 4 and y < x + 6, it is a solution to the system of inequalities.

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