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Which describes the system of equations below? $\newline$ $y = \frac{3}{2}x + 9$ $\newline$ $y = \frac{3}{2}x + \frac{1}{4}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = \frac{3}{2}x + 9

\newline

y = \frac{3}{2}x + \frac{1}{4}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Identify Slope Equality: We have the following system of equations: $\newline$ y = $(\frac{3}{2})x + 9$ $\newline$ y = $(\frac{3}{2})x + \frac{1}{4}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = (\frac{3}{2})x + 9$ , the slope is $\frac{3}{2}$ . $\newline$ In $y = (\frac{3}{2})x + \frac{1}{4}$ , the slope is $\frac{3}{2}$ . $\newline$ Yes, the slopes of both equations are the same.
Identify Y-Intercept Equality: We have: $\newline$ y = $(\frac{3}{2})x + 9$ $\newline$ y = $(\frac{3}{2})x + \frac{1}{4}$ $\newline$ Identify whether the y-intercepts of both the equations are the same. $\newline$ In $y = (\frac{3}{2})x + 9$ , the y-intercept is $9$ . $\newline$ In $y = (\frac{3}{2})x + \frac{1}{4}$ , the y-intercept is $\frac{1}{4}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Choose System Description: $y = \frac{3}{2}x + 9$ $\newline$ $y = \frac{3}{2}x + \frac{1}{4}$ $\newline$ 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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