Is $(1,\ 3)$ a solution to this system of inequalities? $\newline$ $x + 5y > 11$ $\newline$ $6x + 4y < 20$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

Full solution

Q. Is

(1,\ 3)

a solution to this system of inequalities?

\newline

x + 5y > 11

\newline

6x + 4y < 20

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $(1, 3)$ : Does the point $(1, 3)$ satisfy the inequality $x + 5y > 11$ ? $\newline$ Substitute $x = 1$ and $y = 3$ into the inequality $x + 5y > 11$ . $\newline$ $1 + 5 \times 3 > 11$ $\newline$ $1 + 15 > 11$ $\newline$ $16 > 11$ $\newline$ The point $(1, 3)$ satisfies the inequality $x + 5y > 11$ .
Verify Inequality $x + 5y > 11$ : Does the point $(1, 3)$ satisfy the inequality $6x + 4y < 20$ ? $\newline$ Substitute $x = 1$ and $y = 3$ into the inequality $6x + 4y < 20$ . $\newline$ $6 \times 1 + 4 \times 3 < 20$ $\newline$ $6 + 12 < 20$ $\newline$ $18 < 20$ $\newline$ The point $(1, 3)$ satisfies the inequality $6x + 4y < 20$ .
Verify Inequality $6x + 4y < 20$ : Is $(1, 3)$ a solution to the system of inequalities? $\newline$ Since $(1, 3)$ satisfies both inequalities $x + 5y > 11$ and $6x + 4y < 20$ , it is a solution to the system of inequalities.