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Is $(1,9)$ a solution to this system of equations? $\newline$ $y = 5x + 4$ $\newline$ $y = 2x + 7$ $\newline$ 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

(1,9)

a solution to this system of equations?

\newline

y = 5x + 4

\newline

y = 2x + 7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

First Equation Analysis: We have the first equation: $\newline$ $y = 5x + 4$ $\newline$ Does the point $(1, 9)$ satisfy the first equation? $\newline$ $y = 5x + 4$ $\newline$ $9 = 5(1) + 4$ $\newline$ $9 = 5 + 4$ $\newline$ $9 = 9$ $\newline$ Yes, the point $(1, 9)$ satisfies the first equation $y = 5x + 4$ .
Second Equation Analysis: We have the second equation: $\newline$ $y = 2x + 7$ $\newline$ Does the point $(1, 9)$ satisfy the second equation? $\newline$ $y = 2x + 7$ $\newline$ $9 = 2(1) + 7$ $\newline$ $9 = 2 + 7$ $\newline$ $9 = 9$ $\newline$ Yes, the point $(1, 9)$ satisfies the second equation $y = 2x + 7$ .
Solution Verification: We found: $\newline$ $(1, 9)$ satisfies the equation $y = 5x + 4$ . $\newline$ $(1, 9)$ satisfies the equation $y = 2x + 7$ . $\newline$ Is $(1,9)$ a solution to the system of equations? $\newline$ $y = 5x + 4$ $\newline$ $y = 2x + 7$ $\newline$ Both equations are true when $(x, y) = (1, 9)$ . $\newline$ Yes, $(1,9)$ is a solution to the system of equations.

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