Which describes the system of equations below? y = –2x + 5 y = –2x + 7/6 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Analyze slopes of equations: Analyze the slopes of both equations. Equation 1: y = –2x + 5, slope = –2. Equation 2: y = –2x + 7/6, slope = –2. Both equations have the same slope. Compare y-intercepts: Compare the y-intercepts of both equations. Equation 1: y = –2x + 5, y-intercept = 5. Equation 2: y = –2x + 7/6, y-intercept = 7/6. 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 never intersect. This means the system is inconsistent.

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Which describes the system of equations below? $\newline$ $y = -2x + 5$ $\newline$ $y = -2x + \frac{7}{6}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent $\newline$

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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 = -2x + 5

\newline

y = -2x + \frac{7}{6}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

\newline

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ Equation $1$ : $y = -2x + 5$ , slope = $-2$ . $\newline$ Equation $2$ : $y = -2x + \frac{7}{6}$ , slope = $-2$ . $\newline$ Both equations have the same slope.
Compare y-intercepts: Compare the y-intercepts of both equations. $\newline$ Equation $1$ : $y = -2x + 5$ , y-intercept = $5$ . $\newline$ Equation $2$ : $y = -2x + \frac{7}{6}$ , y-intercept = $\frac{7}{6}$ . $\newline$ 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 never intersect. $\newline$ This means the system is inconsistent.