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Is $(3,1)$ a solution to this system of equations? $\newline$ $2x + y = 7$ $\newline$ $2x + 4y = 10$ $\newline$ 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

2x + y = 7

\newline

2x + 4y = 10

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(3, 1)$ satisfies the first equation: $\newline$ $2x + y = 7$ $\newline$ Substitute $x = 3$ and $y = 1$ into the equation: $\newline$ $2(3) + 1 = 7$ $\newline$ $6 + 1 = 7$ $\newline$ $7 = 7$ $\newline$ 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: $\newline$ $2x + 4y = 10$ $\newline$ Substitute $x = 3$ and $y = 1$ into the equation: $\newline$ $2(3) + 4(1) = 10$ $\newline$ $6 + 4 = 10$ $\newline$ $10 = 10$ $\newline$ The point $(3, 1)$ satisfies the second equation.
Confirm Solution: Since the point $(3, 1)$ satisfies both equations in the system, we can conclude that $(3, 1)$ is indeed a solution to the system of equations.

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