Which describes the system of equations below? y = –3x + 1/6 y = –3x + 1/6 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Analyze Equations: Step 1: Analyze the equations given: y = –3x + 1/6 y = –3x + 1/6 Check if the slopes (coefficients of x) are the same in both equations. Both equations have a slope of -3. Check Slopes and Intercepts: Step 2: Check the y-intercepts of both equations: The y-intercept of the first equation is 1/6. The y-intercept of the second equation is also 1/6. 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: Since both equations have the same slope and y-intercept, 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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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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Algebra 1

Classify a system of equations

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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.