Which describes the system of equations below? y = –10x − 6 y = 5/7x + 1/7 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. The first equation is y = –10x − 6, which has a slope of -10. The second equation is y = 5/7x + 1/7, which has a slope of 5/7. Since the slopes are different, the lines are not parallel and will intersect at some point.Determine single solution: Determine if the system has a single solution. Because the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.Determine dependent or independent: Determine if the system is dependent or independent. Since the lines intersect at exactly one point and have different slopes, the system is independent.Choose correct option: Choose the correct option based on the analysis. The system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution.

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Which describes the system of equations below? $\newline$ $y = -10x - 6$ $\newline$ $y = \frac{5}{7}x + \frac{1}{7}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and independent $\newline$ (C)consistent and dependent

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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 = -10x - 6

\newline

y = \frac{5}{7}x + \frac{1}{7}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ The first equation is $y = -10x - 6$ , which has a slope of $-10$ . $\newline$ The second equation is $y = \frac{5}{7}x + \frac{1}{7}$ , which has a slope of $\frac{5}{7}$ . $\newline$ Since the slopes are different, the lines are not parallel and will intersect at some point.
Determine single solution: Determine if the system has a single solution. $\newline$ Because the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.
Determine dependent or independent: Determine if the system is dependent or independent. Since the lines intersect at exactly one point and have different slopes, the system is independent.
Choose correct option: Choose the correct option based on the analysis. $\newline$ The system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution.