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

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Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 6x + 6

\newline

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

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Equation Slopes Same: We have the system of equations: $\newline$ $y = 6x + 6$ $\newline$ $y = 6x + \frac{5}{7}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 6x + 6$ , the slope is $6$ . $\newline$ In $y = 6x + \frac{5}{7}$ , the slope is $6$ . $\newline$ Yes, the slopes of both equations are the same.
Y-Intercepts Different: We have: $\newline$ $y = 6x + 6$ $\newline$ $y = 6x + \frac{5}{7}$ $\newline$ Identify whether the y-intercepts of both the equations are the same. $\newline$ In $y = 6x + 6$ , the y-intercept is $6$ . $\newline$ In $y = 6x + \frac{5}{7}$ , the y-intercept is $\frac{5}{7}$ . $\newline$ No, the y-intercepts of both equations are not the same.
System Inconsistent: $y = 6x + 6$ $\newline$ $y = 6x + \frac{5}{7}$ $\newline$ Choose the option which describes the given system of equations. $\newline$ Since the slopes are the same but the y-intercepts are different, the lines are parallel and never intersect. $\newline$ The system of equations is inconsistent.

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