Which describes the system of equations below? y = –5x − 8 y = –5x − 7/4 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Compare slopes: Compare the slopes of both equations. y = –5x − 8 has a slope of –5. y = –5x − 7/4 also has a slope of –5. Since both slopes are the same, the lines are either parallel or the same line. Compare y-intercepts: Compare the y-intercepts of both equations. y = –5x − 8 has a y-intercept of –8. y = –5x − 7/4 has a y-intercept of –7/4. Since the y-intercepts are different, the lines are parallel and do not intersect. Determine system type: Determine the type of system based on the slopes and y-intercepts. Since the lines are parallel and have different y-intercepts, they never meet. This means the system is inconsistent.

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Which describes the system of equations below? $\newline$ $y = -5x - 8$ $\newline$ $y = -5x - \frac{7}{4}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -5x - 8

\newline

y = -5x - \frac{7}{4}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Compare slopes: Compare the slopes of both equations. $\newline$ $y = -5x - 8$ has a slope of $-5$ . $\newline$ $y = -5x - \frac{7}{4}$ also has a slope of $-5$ . $\newline$ Since both slopes are the same, the lines are either parallel or the same line.
Compare y-intercepts: Compare the y-intercepts of both equations. $\newline$ $y = -5x - 8$ has a y-intercept of $-8$ . $\newline$ $y = -5x - \frac{7}{4}$ has a y-intercept of $-\frac{7}{4}$ . $\newline$ Since the y-intercepts are different, the lines are parallel and do not intersect.
Determine system type: Determine the type of system based on the slopes and $y$ -intercepts. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they never meet. This means the system is inconsistent.