Which describes the system of equations below? y = 8x + 6 y = 4/3x + 2/3 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Analyze slopes: Analyze the slopes of both equations. The first equation is y = 8x + 6, which has a slope of 8. The second equation is y = (4/3)x + (2/3), which has a slope of 4/3. Since the slopes are different (8 ≠ 4/3), the lines are not parallel and they are not the same line.Determine 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 consistent.Dependent or independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line; however, we have already established that the slopes are different, so the lines cannot be the same. Therefore, 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 and the lines are not the same. Therefore, the correct choice is: (C) consistent and independent

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Which describes the system of equations below? $\newline$ $y = 8x + 6$ $\newline$ $y = \frac{4}{3}x + \frac{2}{3}$ $\newline$ 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 = 8x + 6

\newline

y = \frac{4}{3}x + \frac{2}{3}

\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 $y = 8x + 6$ , which has a slope of $8$ . $\newline$ The second equation is $y = \frac{4}{3}x + \frac{2}{3}$ , which has a slope of $\frac{4}{3}$ . $\newline$ Since the slopes are different ( $8 \neq \frac{4}{3}$ ), the lines are not parallel and they are not the same line.
Determine 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 consistent.
Dependent or independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line; however, we have already established that the slopes are different, so the lines cannot be the same. Therefore, 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 and the lines are not the same. Therefore, the correct choice is: $\newline$ (C) consistent and independent