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Which describes the system of equations below? $\newline$ $y = 6x + \frac{2}{5}$ $\newline$ $y = \frac{2}{7}x + \frac{8}{3}$ $\newline$ 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 = 6x + \frac{2}{5}

\newline

y = \frac{2}{7}x + \frac{8}{3}

\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 $y = 6x + \frac{2}{5}$ , the slope is $6$ . $\newline$ For $y = \frac{2}{7}x + \frac{8}{3}$ , the slope is $\frac{2}{7}$ . $\newline$ 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 $y = 6x + \frac{2}{5}$ , the y-intercept is $\frac{2}{5}$ . $\newline$ For $y = \frac{2}{7}x + \frac{8}{3}$ , the y-intercept is $\frac{8}{3}$ . $\newline$ The y-intercepts are different, confirming that the lines will intersect at one point.

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