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Is $(2,1)$ a solution to this system of equations? $\newline$ $5x + 7y = 17$ $\newline$ $3x + y = 7$ $\newline$ 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

(2,1)

a solution to this system of equations?

\newline

5x + 7y = 17

\newline

3x + y = 7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(2, 1)$ satisfies the first equation: $\newline$ $5x + 7y = 17$ $\newline$ Substitute $x = 2$ and $y = 1$ into the equation: $\newline$ $5(2) + 7(1) = 17$ $\newline$ $10 + 7 = 17$ $\newline$ $17 = 17$ $\newline$ The point $(2, 1)$ satisfies the first equation.
Check Second Equation: Now, we need to check if the point $(2, 1)$ satisfies the second equation: $\newline$ $3x + y = 7$ $\newline$ Substitute $x = 2$ and $y = 1$ into the equation: $\newline$ $3(2) + 1 = 7$ $\newline$ $6 + 1 = 7$ $\newline$ $7 = 7$ $\newline$ The point $(2, 1)$ satisfies the second equation.
Confirm Solution: Since the point $(2, 1)$ satisfies both equations in the system, we can conclude that $(2,1)$ is indeed a solution to the system of equations.

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