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Which describes the system of equations below? $\newline$ $y = -\frac{6}{7}x - 6$ $\newline$ $y = \frac{6}{5}x - \frac{6}{7}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (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{6}{7}x - 6

\newline

y = \frac{6}{5}x - \frac{6}{7}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Identify slopes: Step $1$ : Identify the slopes of both equations. $\newline$ For $y = -\frac{6}{7}x - 6$ , the slope is $-\frac{6}{7}$ . $\newline$ For $y = \frac{6}{5}x - \frac{6}{7}$ , the slope is $\frac{6}{5}$ . $\newline$ Since $-\frac{6}{7}$ is not equal to $\frac{6}{5}$ , the slopes are different.
Check y-intercepts: Step $2$ : Check if the y-intercepts are the same. $\newline$ For $y = -\frac{6}{7}x - 6$ , the y-intercept is $-6$ . $\newline$ For $y = \frac{6}{5}x - \frac{6}{7}$ , the y-intercept is $-\frac{6}{7}$ . $\newline$ Since $-6$ is not equal to $-\frac{6}{7}$ , the y-intercepts are different.
Determine system type: Step $3$ : Determine the type of system based on slopes and $y$ -intercepts. $\newline$ Since the slopes are different, the lines are not parallel and will intersect at one point. $\newline$ This means the system is consistent and has exactly one solution, making it independent.

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