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Is $(1,1)$ a solution to this system of equations? $\newline$ $4x + 10y = 14$ $\newline$ $x + 6y = 7$ $\newline$ 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

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(1, 1)$ satisfies the first equation: $\newline$ $4x + 10y = 14$ $\newline$ Substitute $x = 1$ and $y = 1$ into the equation: $\newline$ $4(1) + 10(1) = 14$ $\newline$ $4 + 10 = 14$ $\newline$ $14 = 14$ $\newline$ 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: $\newline$ $x + 6y = 7$ $\newline$ Substitute $x = 1$ and $y = 1$ into the equation: $\newline$ $1(1) + 6(1) = 7$ $\newline$ $1 + 6 = 7$ $\newline$ $7 = 7$ $\newline$ The point $(1, 1)$ satisfies the second equation.
Conclude Solution: 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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