Which describes the system of equations below? y = –4x − 1 y = –4x − 7/8 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Compare slopes: Compare the slopes of both equations. Equation 1: y = –4x − 1, slope = –4. Equation 2: y = –4x − 7/8, slope = –4. Both equations have the same slope. Compare y-intercepts: Compare the y-intercepts of both equations. Equation 1: y = –4x − 1, y-intercept = −1. Equation 2: y = –4x − 7/8, y-intercept = −7/8. The y-intercepts are different. Determine system type: Determine the type of system based on slopes and y-intercepts. Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. This means the system is inconsistent.

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Which describes the system of equations below? $\newline$ $y = -4x - 1$ $\newline$ $y = -4x - \frac{7}{8}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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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 = -4x - 1

\newline

y = -4x - \frac{7}{8}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Compare slopes: Compare the slopes of both equations. $\newline$ Equation $1$ : $y = -4x - 1$ , slope = $-4$ . $\newline$ Equation $2$ : $y = -4x - \frac{7}{8}$ , slope = $-4$ . $\newline$ Both equations have the same slope.
Compare y-intercepts: Compare the y-intercepts of both equations. $\newline$ Equation $1$ : $y = -4x - 1$ , y-intercept = $-1$ . $\newline$ Equation $2$ : $y = -4x - \frac{7}{8}$ , y-intercept = $-\frac{7}{8}$ . $\newline$ The y-intercepts are different.
Determine system type: Determine the type of system based on slopes and $y$ -intercepts. $\newline$ Since the slopes are the same but the $y$ -intercepts are different, the lines are parallel and do not intersect. $\newline$ This means the system is inconsistent.