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Is $(3,1)$ a solution to this system of equations? $\newline$ $3x + 3y = 12$ $\newline$ $12x + y = 13$ $\newline$ 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

(3,1)

a solution to this system of equations?

\newline

3x + 3y = 12

\newline

12x + y = 13

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(3, 1)$ satisfies the first equation: $\newline$ $3x + 3y = 12$ $\newline$ Substitute $x = 3$ and $y = 1$ into the equation: $\newline$ $3(3) + 3(1) = 12$ $\newline$ $9 + 3 = 12$ $\newline$ $12 = 12$ $\newline$ The point $(3, 1)$ satisfies the first equation.
Check Second Equation: Now, we need to check if the point $(3, 1)$ satisfies the second equation: $\newline$ $12x + y = 13$ $\newline$ Substitute $x = 3$ and $y = 1$ into the equation: $\newline$ $12(3) + 1 = 13$ $\newline$ $36 + 1 = 13$ $\newline$ $37 \neq 13$ $\newline$ The point $(3, 1)$ does not satisfy the second equation.

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