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Which describes the system of equations below? $\newline$ $y = -5x + 2$ $\newline$ $y = -5x + 2$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (C)consistent and independent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -5x + 2

\newline

y = -5x + 2

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Analyze Equations: Analyze the equations to see if they are the same or different. $\newline$ We have: $\newline$ $y = -5x + 2$ $\newline$ $y = -5x + 2$ $\newline$ Both equations are identical, meaning they represent the same line.
Check Slopes and Intercepts: Check the slopes and $y$ -intercepts of both equations. $\newline$ For $y = -5x + 2$ , the slope is $-5$ and the $y$ -intercept is $2$ . $\newline$ For $y = -5x + 2$ , the slope is $-5$ and the $y$ -intercept is $2$ . $\newline$ Both the slope and $y$ -intercept are the same for both equations.
Determine System Type: Determine the type of system based on the analysis. $\newline$ Since both equations are identical, they represent the same line. This means every solution of one equation is a solution of the other, hence the system is consistent and dependent.

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