Which describes the system of equations below? y = 9/7x − 5/3 y = 7/8x + 8/5 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. The first equation is y = (9/7)x - (5/3). The slope of this line is 9/7. The second equation is y = (7/8)x + (8/5). The slope of this line is 7/8. Since the slopes are different (9/7 ≠ 7/8), the lines are not parallel and will intersect at exactly one point.Determine Single Solution: Determine if the system has a single solution. Since the slopes are different, the lines will intersect at one point. This means there is one solution to the system of equations.Conclude System Type: Conclude the type of system based on the number of solutions. Because there is exactly one solution, the system is consistent (it has at least one solution) and independent (it has exactly one solution).

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Which describes the system of equations below? $\newline$ $y = \frac{9}{7}x - \frac{5}{3}$ $\newline$ $y = \frac{7}{8}x + \frac{8}{5}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (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}{7}x - \frac{5}{3}

\newline

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

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = \frac{9}{7}x - \frac{5}{3}$ . The slope of this line is $\frac{9}{7}$ . $\newline$ The second equation is $y = \frac{7}{8}x + \frac{8}{5}$ . The slope of this line is $\frac{7}{8}$ . $\newline$ Since the slopes are different ( $\frac{9}{7} \neq \frac{7}{8}$ ), the lines are not parallel and will intersect at exactly one point.
Determine Single Solution: Determine if the system has a single solution. $\newline$ Since the slopes are different, the lines will intersect at one point. This means there is one solution to the system of equations.
Conclude System Type: Conclude the type of system based on the number of solutions. Because there is exactly $1$ solution, the system is consistent (it has at least one solution) and independent (it has exactly $1$ solution).