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Is $(1,2)$ a solution to this system of equations? $\newline$ $3x + 8y = 19$ $\newline$ $x + 4y = 9$ $\newline$ 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

(1,2)

a solution to this system of equations?

\newline

3x + 8y = 19

\newline

x + 4y = 9

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(1, 2)$ satisfies the first equation: $\newline$ $3x + 8y = 19$ $\newline$ Substitute $x = 1$ and $y = 2$ into the equation: $\newline$ $3(1) + 8(2) = 19$ $\newline$ $3 + 16 = 19$ $\newline$ $19 = 19$ $\newline$ The point $(1, 2)$ satisfies the first equation.
Check Second Equation: Now, we need to check if the point $(1, 2)$ satisfies the second equation: $\newline$ $x + 4y = 9$ $\newline$ Substitute $x = 1$ and $y = 2$ into the equation: $\newline$ $1 + 4(2) = 9$ $\newline$ $1 + 8 = 9$ $\newline$ $9 = 9$ $\newline$ The point $(1, 2)$ satisfies the second equation.
Conclude Solution: Since the point $(1, 2)$ satisfies both equations in the system, we can conclude that $(1, 2)$ is indeed a solution to the system of equations.

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