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Is $(1,5)$ a solution to this system of equations? $\newline$ $5x + 3y = 20$ $\newline$ $x + 2y = 11$ $\newline$ 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

(1,5)

a solution to this system of equations?

\newline

5x + 3y = 20

\newline

x + 2y = 11

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: We need to check if the point $(1, 5)$ satisfies the first equation: $\newline$ $5x + 3y = 20$ $\newline$ Substitute $x = 1$ and $y = 5$ into the equation: $\newline$ $5(1) + 3(5) = 20$ $\newline$ $5 + 15 = 20$ $\newline$ $20 = 20$ $\newline$ The point $(1, 5)$ satisfies the first equation.
Check Second Equation: Now, we need to check if the point $(1, 5)$ satisfies the second equation: $\newline$ $x + 2y = 11$ $\newline$ Substitute $x = 1$ and $y = 5$ into the equation: $\newline$ $1 + 2(5) = 11$ $\newline$ $1 + 10 = 11$ $\newline$ $11 = 11$ $\newline$ The point $(1, 5)$ satisfies the second equation.
Conclusion: Since the point $(1, 5)$ satisfies both equations in the system, we can conclude that $(1, 5)$ is indeed a solution to the system of equations.

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