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Which describes the system of equations below? $\newline$ $y = \frac{9}{5}x - 8$ $\newline$ $y = \frac{9}{5}x - \frac{4}{9}$ $\newline$ 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{9}{5}x - 8

\newline

y = \frac{9}{5}x - \frac{4}{9}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Identify Slopes: We have the system of equations: $\newline$ y = $(\frac{9}{5})x - 8$ $\newline$ y = $(\frac{9}{5})x - \frac{4}{9}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = (\frac{9}{5})x - 8$ , the slope is $\frac{9}{5}$ . $\newline$ In $y = (\frac{9}{5})x - \frac{4}{9}$ , the slope is $\frac{9}{5}$ . $\newline$ Yes, the slopes of both equations are the same.
Identify Y-Intercepts: We have: $\newline$ y = $(\frac{9}{5})x - 8$ $\newline$ y = $(\frac{9}{5})x - \frac{4}{9}$ $\newline$ Identify whether the y-intercepts of both the equations are the same. $\newline$ In $y = (\frac{9}{5})x - 8$ , the y-intercept is $-8$ . $\newline$ In $y = (\frac{9}{5})x - \frac{4}{9}$ , the y-intercept is $-\frac{4}{9}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Choose Description: $y = \frac{9}{5}x - 8$ $\newline$ $y = \frac{9}{5}x - \frac{4}{9}$ $\newline$ 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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