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Is $(1,1)$ a solution to this system of equations? $\newline$ $9x + y = 10$ $\newline$ $6x + 5y = 11$ $\newline$ 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

(1,1)

a solution to this system of equations?

\newline

9x + y = 10

\newline

6x + 5y = 11

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(1, 1)$ satisfies the first equation: $\newline$ $9x + y = 10$ $\newline$ Substitute $x = 1$ and $y = 1$ into the equation: $\newline$ $9(1) + 1 = 10$ $\newline$ $9 + 1 = 10$ $\newline$ $10 = 10$ $\newline$ The point $(1, 1)$ satisfies the first equation.
Check Second Equation: Now, we need to check if the point $(1, 1)$ satisfies the second equation: $\newline$ $6x + 5y = 11$ $\newline$ Substitute $x = 1$ and $y = 1$ into the equation: $\newline$ $6(1) + 5(1) = 11$ $\newline$ $6 + 5 = 11$ $\newline$ $11 = 11$ $\newline$ The point $(1, 1)$ satisfies the second equation.
Conclusion: Since the point $(1, 1)$ satisfies both equations in the system, we can conclude that $(1, 1)$ is indeed a solution to the system of equations.

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