Which describes the system of equations below? y = –2x + 1/5 y = 3/10x + 4/3 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. The first equation is y = –2x + 1/5, which has a slope of –2. The second equation is y = 3/10x + 4/3, which has a slope of 3/10. Since the slopes are different, the lines are not parallel and will intersect at one point.Determine single solution: Determine if the system has a single solution. Because the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.Determine dependent or independent: Determine if the system is dependent or independent. Since the lines intersect at exactly one point, they are not the same line, and thus the system is independent.

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Which describes the system of equations below? $\newline$ $y = -2x + \frac{1}{5}$ $\newline$ $y = \frac{3}{10}x + \frac{4}{3}$ $\newline$ 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 = -2x + \frac{1}{5}

\newline

y = \frac{3}{10}x + \frac{4}{3}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ The first equation is $y = -2x + \frac{1}{5}$ , which has a slope of $-2$ . $\newline$ The second equation is $y = \frac{3}{10}x + \frac{4}{3}$ , which has a slope of $\frac{3}{10}$ . $\newline$ Since the slopes are different, the lines are not parallel and will intersect at one point.
Determine single solution: Determine if the system has a single solution. $\newline$ Because the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.
Determine dependent or independent: Determine if the system is dependent or independent. Since the lines intersect at exactly one point, they are not the same line, and thus the system is independent.