Which describes the system of equations below? y = –10x − 5/3 y = 1/2x − 2/5 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. The slope of the first equation y = –10x − 5/3 is –10. The slope of the second equation y = 1/2x − 2/5 is 1/2. Since the slopes are different, the lines are not parallel and they will intersect at one point.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.Dependent or Independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line. Since the slopes are different, the lines are not the same, and thus the system is independent.

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Which describes the system of equations below? $\newline$ $y = -10x - \frac{5}{3}$ $\newline$ $y = \frac{1}{2}x - \frac{2}{5}$ $\newline$ 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 = -10x - \frac{5}{3}

\newline

y = \frac{1}{2}x - \frac{2}{5}

\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 slope of the first equation $y = -10x - \frac{5}{3}$ is $-10$ . $\newline$ The slope of the second equation $y = \frac{1}{2}x - \frac{2}{5}$ is $\frac{1}{2}$ . $\newline$ Since the slopes are different, the lines are not parallel and they will intersect at one point.
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.
Dependent or Independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line. Since the slopes are different, the lines are not the same, and thus the system is independent.