Which describes the system of equations below? y = 1/7x + 9/5 y = 7/9x + 9/2 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes: Analyze the slopes of both equations. The first equation is y = (1/7)x + (9/5). The slope of this line is 1/7. The second equation is y = (7/9)x + (9/2). The slope of this line is 7/9. Since the slopes are different (1/7 ≠ 7/9), the lines are not parallel and will intersect at one point.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 therefore consistent.Nature of system: Determine the nature of the system. Because the system has a single solution and the lines are not the same (they have different slopes and y-intercepts), 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. Therefore, the correct choice is (B) consistent and independent.

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Which describes the system of equations below? $\newline$ $y = \frac{1}{7}x + \frac{9}{5}$ $\newline$ $y = \frac{7}{9}x + \frac{9}{2}$ $\newline$ 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 = \frac{1}{7}x + \frac{9}{5}

\newline

y = \frac{7}{9}x + \frac{9}{2}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Analyze slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = \frac{1}{7}x + \frac{9}{5}$ . The slope of this line is $\frac{1}{7}$ . $\newline$ The second equation is $y = \frac{7}{9}x + \frac{9}{2}$ . The slope of this line is $\frac{7}{9}$ . $\newline$ Since the slopes are different ( $\frac{1}{7} \neq \frac{7}{9}$ ), the lines are not parallel and will intersect at one point.
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 therefore consistent.
Nature of system: Determine the nature of the system. $\newline$ Because the system has a single solution and the lines are not the same (they have different slopes and $y$ -intercepts), 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. Therefore, the correct choice is $(B)$ consistent and independent.