Which describes the system of equations below? y = 6x − 3/4 y = –7/5x − 3/10 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze Slopes: Analyze the slopes of both equations. The first equation is y = 6x − 3/4, which has a slope of 6. The second equation is y = –7/5x − 3/10, which has a slope of –7/5. Since the slopes are different (6 ≠ –7/5), the lines are not parallel.Determine Solutions: Determine if the system has any solutions. Because the slopes are different, the lines will intersect at exactly one point. This means the system has one solution and is therefore consistent.Nature of System: Determine the nature of the system. Since the system has exactly one solution, the equations are 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? $\newline$ $y = 6x - \frac{3}{4}$ $\newline$ $y = -\frac{7}{5}x - \frac{3}{10}$ $\newline$ 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 = 6x - \frac{3}{4}

\newline

y = -\frac{7}{5}x - \frac{3}{10}

\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 $y = 6x − \frac{3}{4}$ , which has a slope of $6$ . $\newline$ The second equation is $y = −\frac{7}{5}x − \frac{3}{10}$ , which has a slope of $−\frac{7}{5}$ . $\newline$ Since the slopes are different ( $6 ≠ −\frac{7}{5}$ ), the lines are not parallel.
Determine Solutions: Determine if the system has any solutions. $\newline$ Because the slopes are different, the lines will intersect at exactly one point. $\newline$ This means the system has one solution and is therefore consistent.
Nature of System: Determine the nature of the system. $\newline$ Since the system has exactly one solution, the equations are 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.