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Which describes the system of equations below? $\newline$ $y = -3x + \frac{1}{6}$ $\newline$ $y = -3x + \frac{1}{6}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -3x + \frac{1}{6}

\newline

y = -3x + \frac{1}{6}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Analyze Equations: Step $1$ : Analyze the equations given: $\newline$ $y = -3x + \frac{1}{6}$ $\newline$ $y = -3x + \frac{1}{6}$ $\newline$ Check if the slopes (coefficients of $x$ ) are the same in both equations. $\newline$ Both equations have a slope of $-3$ .
Check Slopes and Intercepts: Step $2$ : Check the $y$ -intercepts of both equations: $\newline$ The $y$ -intercept of the first equation is $\frac{1}{6}$ . $\newline$ The $y$ -intercept of the second equation is also $\frac{1}{6}$ . $\newline$ Since both $y$ -intercepts are the same, the lines are identical.
Determine System Type: Step $3$ : Determine the type of system based on the slopes and $y$ -intercepts: $\newline$ Since both equations have the same slope and $y$ -intercept, they represent the same line. $\newline$ This means every solution of one equation is a solution of the other, hence the system is consistent and dependent.

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