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Which describes the system of equations below? $\newline$ $y = -5x - 9$ $\newline$ $y = -5x + \frac{1}{10}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -5x - 9

\newline

y = -5x + \frac{1}{10}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify Slopes: We have the system of equations: $\newline$ $y = -5x - 9$ $\newline$ $y = -5x + \frac{1}{10}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -5x - 9$ , the slope is $-5$ . $\newline$ In $y = -5x + \frac{1}{10}$ , the slope is also $-5$ . $\newline$ Yes, the slopes of both the equations are the same.
Identify Y-Intercepts: We have: $\newline$ y = $-5x - 9$ $\newline$ y = $-5x + \frac{1}{10}$ $\newline$ Identify whether the y-intercepts of both the equations are the same. $\newline$ In $y = -5x - 9$ , the y-intercept is $-9$ . $\newline$ In $y = -5x + \frac{1}{10}$ , the y-intercept is $\frac{1}{10}$ . $\newline$ No, the y-intercepts of both the equations are not the same.
Choose Option: $y = -5x - 9$ $\newline$ $y = -5x + \frac{1}{10}$ $\newline$ 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 will never intersect. $\newline$ This means the system has no solution and is therefore inconsistent.

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