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

(4,10)

a solution to this system of equations?

\newline

y = 2x + 2

\newline

y = 10x + 1

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check First Equation: First, we need to check if the point $(4,10)$ satisfies the first equation $y = 2x + 2$ . Substitute $x$ with $4$ and see if we get $y$ as $10$ . $y = 2(4) + 2$ $y = 8 + 2$ $y = 10$ Since the calculated $y$ value is $10$ , which is the $y$ -coordinate of the point $(4,10)$ , the point satisfies the first equation.
Check Second Equation: Next, we need to check if the point $(4,10)$ satisfies the second equation $y = 10x + 1$ . Substitute $x$ with $4$ and see if we get $y$ as $10$ . $y = 10(4) + 1$ $y = 40 + 1$ $y = 41$ Since the calculated $y$ value is $y = 10x + 1$ $0$ , which is not the $y$ -coordinate of the point $(4,10)$ , the point does not satisfy the second equation.
Final Evaluation: Since the point $(4,10)$ does not satisfy both equations of the system, it is not a solution to the system of equations.

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