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Which describes the system of equations below? $\newline$ $y = 3x + \frac{5}{2}$ $\newline$ $y = \frac{1}{8}x + \frac{5}{7}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = 3x + \frac{5}{2}

\newline

y = \frac{1}{8}x + \frac{5}{7}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Identify slopes: Step $1$ : Identify the slopes of both equations. $\newline$ For $y = 3x + \frac{5}{2}$ , the slope is $3$ . $\newline$ For $y = \frac{1}{8}x + \frac{5}{7}$ , the slope is $\frac{1}{8}$ . $\newline$ Since the slopes are different, the lines are not parallel and will intersect at one point.
Check y-intercepts: Step $2$ : Check if the y-intercepts are the same. $\newline$ For $y = 3x + \frac{5}{2}$ , the y-intercept is $\frac{5}{2}$ . $\newline$ For $y = \frac{1}{8}x + \frac{5}{7}$ , the y-intercept is $\frac{5}{7}$ . $\newline$ The y-intercepts are different, confirming that the lines will intersect at only one point.
Determine system type: Step $3$ : Determine the type of system based on the slopes and $y$ -intercepts. $\newline$ Since the lines have different slopes and different $y$ -intercepts, they will intersect at exactly one point. This means the system of equations has one solution and is therefore consistent and independent.

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