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Is $(1,\ 4)$ a solution to this system of inequalities? $\newline$ 6x + y < 13 $\newline$ 5x + 3y > 20 $\newline$ 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,\ 4)

a solution to this system of inequalities?

\newline

6x + y < 13

\newline

5x + 3y > 20

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check First Inequality: Does the point $(1, 4)$ satisfy the inequality 6x + y < 13? $\newline$ Substitute $1$ for $x$ and $4$ for $y$ in 6x + y < 13. $\newline$ 6(1) + 4 < 13 $\newline$ 6 + 4 < 13 $\newline$ 10 < 13 $\newline$ Since 10 < 13 is true, $(1, 4)$ satisfies the first inequality.
Check Second Inequality: Does the point $(1, 4)$ satisfy the inequality 5x + 3y > 20? $\newline$ Substitute $1$ for $x$ and $4$ for $y$ in 5x + 3y > 20. $\newline$ 5(1) + 3(4) > 20 $\newline$ 5 + 12 > 20 $\newline$ 17 > 20 $\newline$ Since 17 > 20 is false, $(1, 4)$ does not satisfy the second inequality.
Verify Solution to System: Is $(1, 4)$ a solution to the system of inequalities? $\newline$ For a point to be a solution to a system of inequalities, it must satisfy all inequalities in the system. Since $(1, 4)$ does not satisfy the second inequality, it is not a solution to the system.

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