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Is $(2,\,2)$ a solution to this system of inequalities? $\newline$ $5x + 4y \leq 18$ $\newline$ $2x + y \leq 6$ $\newline$ 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

(2,\,2)

a solution to this system of inequalities?

\newline

5x + 4y \leq 18

\newline

2x + y \leq 6

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $2, 2$ : Does the point $2, 2$ satisfy the inequality $5x + 4y \leq 18$ ? $\newline$ Substitute $2$ for $x$ and $2$ for $y$ in $5x + 4y \leq 18$ . $\newline$ $5(2) + 4(2) \leq 18$ $\newline$ $10 + 8 \leq 18$ $\newline$ $2, 2$ $0$ $\newline$ Since $2, 2$ $0$ is true, $2, 2$ satisfies the inequality $5x + 4y \leq 18$ .
Verify Inequality $5x + 4y \leq 18$ : Does the point $(2, 2)$ satisfy the inequality $2x + y \leq 6$ ? $\newline$ Substitute $2$ for $x$ and $2$ for $y$ in $2x + y \leq 6$ . $\newline$ $2(2) + 2 \leq 6$ $\newline$ $4 + 2 \leq 6$ $\newline$ $(2, 2)$ $0$ $\newline$ Since $(2, 2)$ $0$ is true, $(2, 2)$ satisfies the inequality $2x + y \leq 6$ .
Verify Inequality $2x + y \leq 6$ : Is $(2, 2)$ a solution to the system of inequalities? $\newline$ Since $(2, 2)$ satisfies both inequalities $5x + 4y \leq 18$ and $2x + y \leq 6$ , $(2, 2)$ is a solution to the system of inequalities.

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