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Is $(1,7)$ a solution to this system of equations? $\newline$ $x + 2y = 15$ $\newline$ $2x + 2y = 16$ $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Is (x, y) a solution to the system of equations?

Full solution

Q. Is

(1,7)

a solution to this system of equations?

\newline

x + 2y = 15

\newline

2x + 2y = 16

\newline

Choices:

\newline

(A) yes

\newline

(B) no

First Equation Check: We have the first equation: $\newline$ $x + 2y = 15$ $\newline$ Does the point $(1, 7)$ satisfy the first equation? $\newline$ $x + 2y = 15$ $\newline$ $1 + 2(7) = 15$ $\newline$ $1 + 14 = 15$ $\newline$ $15 = 15$ $\newline$ Yes, the point $(1, 7)$ satisfies the first equation.
Second Equation Check: We have the second equation: $\newline$ $2x + 2y = 16$ $\newline$ Does the point $(1, 7)$ satisfy the second equation? $\newline$ $2x + 2y = 16$ $\newline$ $2(1) + 2(7) = 16$ $\newline$ $2 + 14 = 16$ $\newline$ $16 = 16$ $\newline$ Yes, the point $(1, 7)$ satisfies the second equation.
Final Solution Verification: We found: $\newline$ $(1, 7)$ satisfies the equation $x + 2y = 15$ . $\newline$ $(1, 7)$ satisfies the equation $2x + 2y = 16$ . $\newline$ Is $(1,7)$ a solution to the system of equations? $\newline$ $x + 2y = 15$ $\newline$ $2x + 2y = 16$ $\newline$ Both equations are true when $(x, y) = (1, 7)$ . $\newline$ Yes, $(1,7)$ is a solution to the system of equations.

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