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Which describes the system of equations below? $\newline$ $y = \frac{1}{4}x + 5$ $\newline$ $y = \frac{1}{4}x + 5$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (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 = \frac{1}{4}x + 5

\newline

y = \frac{1}{4}x + 5

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Analyze Equations: Step $1$ : Analyze the equations given. $\newline$ We have: $\newline$ $y = \frac{1}{4}x + 5$ $\newline$ $y = \frac{1}{4}x + 5$ $\newline$ Check if the slopes of both equations are the same. $\newline$ Slope of the first equation is $\frac{1}{4}$ . $\newline$ Slope of the second equation is $\frac{1}{4}$ .
Check Slopes and Intercepts: Step $2$ : Check the $y$ -intercepts of both equations. $y = \frac{1}{4}x + 5$ has a $y$ -intercept of $5$ . $y = \frac{1}{4}x + 5$ also has a $y$ -intercept of $5$ .
Determine Relationship: Step $3$ : Determine the relationship between the equations. $\newline$ Since both the slope and $y$ -intercept are the same for both equations, they represent the same line. This means every solution of one equation is a solution of the other, hence they are dependent.

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