Which describes the system of equations below? y = –x − 5 y = –x + 5/7 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify Slopes: We have the following system of equations: y = –x − 5 y = –x + 5/7 Identify whether the slopes of both the equations are the same. In y = –x − 5, the slope is -1. In y = –x + 5/7, the slope is also -1. Yes, the slopes of both equations are the same. Identify Y-Intercepts: Now, identify whether the y-intercepts of both equations are the same. In y = –x − 5, the y-intercept is -5. In y = –x + 5/7, the y-intercept is 5/7. No, the y-intercepts of both equations are not the same. Determine Line Relationship: Since the slopes are the same but the y-intercepts are different, the lines are parallel to each other and never intersect. Choose the option which describes the given system of equations. The system of equations is inconsistent because there is no point that satisfies both equations simultaneously.

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

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Math Problems

Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -x - 5

\newline

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

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify Slopes: We have the following system of equations: $\newline$ $y = -x - 5$ $\newline$ $y = -x + \frac{5}{7}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -x - 5$ , the slope is $-1$ . $\newline$ In $y = -x + \frac{5}{7}$ , the slope is also $-1$ . $\newline$ Yes, the slopes of both equations are the same.
Identify Y-Intercepts: Now, identify whether the y-intercepts of both equations are the same. $\newline$ In $y = -x - 5$ , the y-intercept is $-5$ . $\newline$ In $y = -x + \frac{5}{7}$ , the y-intercept is $\frac{5}{7}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Determine Line Relationship: Since the slopes are the same but the $y$ -intercepts are different, the lines are parallel to each other and never intersect. $\newline$ Choose the option which describes the given system of equations. $\newline$ The system of equations is inconsistent because there is no point that satisfies both equations simultaneously.