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Which describes the system of equations below? $\newline$ $y = \frac{4}{3}x + \frac{5}{6}$ $\newline$ $y = \frac{2}{7}x + \frac{1}{8}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{4}{3}x + \frac{5}{6}

\newline

y = \frac{2}{7}x + \frac{1}{8}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Compare slopes: We have the following system of equations: $\newline$ $y = \frac{4}{3}x + \frac{5}{6}$ $\newline$ $y = \frac{2}{7}x + \frac{1}{8}$ $\newline$ First, we need to compare the slopes of both equations to determine if they are the same or different. $\newline$ The slope of the first equation is $\frac{4}{3}$ . $\newline$ The slope of the second equation is $\frac{2}{7}$ . $\newline$ Since $\frac{4}{3} \neq \frac{2}{7}$ , the slopes are different.
Determine intersection point: Since the slopes are different, we can conclude that the lines represented by these equations are not parallel and will intersect at exactly one point. This means that the system of equations has one solution where the two lines intersect. Therefore, the system is consistent because it has at least one solution, and it is independent because it has exactly one solution.

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