Which describes the system of equations below? y = 2x − 7/5 y = 8/3x + 8/5 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Analyze System of Equations: Analyze the given system of equations to determine its type. We have two equations: y = 2x − 7/5 y = 8/3x + 8/5 To determine if the system is consistent and independent, inconsistent, or consistent and dependent, we need to compare the slopes and y-intercepts of the two lines represented by these equations.Compare Slopes: Compare the slopes of the two equations. The slope of the first equation (y = 2x − 7/5) is 2. The slope of the second equation (y = 8/3x + 8/5) is 8/3. Since the slopes are different (2 ≠ 8/3), the lines are not parallel and therefore they will intersect at exactly one point. This means the system is consistent and has a unique solution.Determine Consistency: Since the slopes are different, we do not need to compare the y-intercepts to determine the type of system. The system is consistent and independent because the lines will intersect at exactly one point.

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Which describes the system of equations below? $\newline$ $y = 2x - \frac{7}{5}$ $\newline$ $y = \frac{8}{3}x + \frac{8}{5}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Grade 8

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 2x - \frac{7}{5}

\newline

y = \frac{8}{3}x + \frac{8}{5}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Analyze System of Equations: Analyze the given system of equations to determine its type. $\newline$ We have two equations: $\newline$ $y = 2x − \frac{7}{5}$ $\newline$ $y = \frac{8}{3}x + \frac{8}{5}$ $\newline$ To determine if the system is consistent and independent, inconsistent, or consistent and dependent, we need to compare the slopes and $y$ -intercepts of the two lines represented by these equations.
Compare Slopes: Compare the slopes of the two equations. $\newline$ The slope of the first equation $y = 2x - \frac{7}{5}$ is $2$ . $\newline$ The slope of the second equation $y = \frac{8}{3}x + \frac{8}{5}$ is $\frac{8}{3}$ . $\newline$ Since the slopes are different $2 \neq \frac{8}{3}$ , the lines are not parallel and therefore they will intersect at exactly one point. $\newline$ This means the system is consistent and has a unique solution.
Determine Consistency: Since the slopes are different, we do not need to compare the $y$ -intercepts to determine the type of system. $\newline$ The system is consistent and independent because the lines will intersect at exactly one point.