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Which describes the system of equations below? $\newline$ $y = 6x - 8$ $\newline$ $y = 6x - \frac{7}{4}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = 6x - 8

\newline

y = 6x - \frac{7}{4}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify Slopes: Identify the slopes of both equations. $\newline$ For $y = 6x - 8$ , the slope is $6$ . $\newline$ For $y = 6x - \frac{7}{4}$ , the slope is also $6$ . $\newline$ Both equations have the same slope.
Compare Y-Intercepts: Compare the y-intercepts of both equations. $\newline$ For $y = 6x - 8$ , the y-intercept is $-8$ . $\newline$ For $y = 6x - \frac{7}{4}$ , the y-intercept is $-\frac{7}{4}$ . $\newline$ The y-intercepts are different.
Determine System Type: Determine the type of system based on slopes and $y$ -intercepts. $\newline$ Since the slopes are the same but the $y$ -intercepts are different, the lines are parallel and do not intersect. $\newline$ This means the system has no solution.

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