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Is $(5,\,3)$ a solution to this system of inequalities? $\newline$ 2x + 2y < 19 $\newline$ $3x + y \leq 18$ $\newline$ 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

(5,\,3)

a solution to this system of inequalities?

\newline

2x + 2y < 19

\newline

3x + y \leq 18

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check First Inequality: Check if $(5, 3)$ satisfies the first inequality 2x + 2y < 19. $\newline$ Substitute $x = 5$ and $y = 3$ into the inequality. $\newline$ 2(5) + 2(3) < 19 $\newline$ 10 + 6 < 19 $\newline$ 16 < 19 $\newline$ This is true.
Check Second Inequality: Check if $(5, 3)$ satisfies the second inequality $3x + y \leq 18$ . Substitute $x = 5$ and $y = 3$ into the inequality. $3(5) + 3 \leq 18$ $15 + 3 \leq 18$ $18 \leq 18$ This is also true.
Solution Verification: Since $(5, 3)$ satisfies both inequalities, it is a solution to the system.

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