Which describes the system of equations below? y = –9/5x − 5 y = 8/7x − 7/5 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. The first equation is y = –9/5x – 5, which has a slope of –9/5. The second equation is y = 8/7x – 7/5, which has a slope of 8/7. Since the slopes are different, the lines are not parallel and will intersect at one point.Single Solution: Determine if the system has a single solution. Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.Dependent or Independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line, which would mean they have the same slope and y-intercept. Since we have already established that the slopes are different, the lines are not the same, and the system is not dependent.Conclude System Type: Conclude the type of system based on the previous steps. Since the system is consistent and has exactly one solution, and the lines are not the same (not dependent), the system is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = -\frac{9}{5}x - 5$ $\newline$ $y = \frac{8}{7}x - \frac{7}{5}$ $\newline$ 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 = -\frac{9}{5}x - 5

\newline

y = \frac{8}{7}x - \frac{7}{5}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = \frac{-9}{5}x - 5$ , which has a slope of $\frac{-9}{5}$ . $\newline$ The second equation is $y = \frac{8}{7}x - \frac{7}{5}$ , which has a slope of $\frac{8}{7}$ . $\newline$ Since the slopes are different, the lines are not parallel and will intersect at one point.
Single Solution: Determine if the system has a single solution. $\newline$ Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.
Dependent or Independent: Determine if the system is dependent or independent. $\newline$ A system is dependent if the equations represent the same line, which would mean they have the same slope and $y$ -intercept. Since we have already established that the slopes are different, the lines are not the same, and the system is not dependent.
Conclude System Type: Conclude the type of system based on the previous steps. $\newline$ Since the system is consistent and has exactly one solution, and the lines are not the same (not dependent), the system is consistent and independent.