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Which describes the system of equations below? $\newline$ $y = -9x - 8$ $\newline$ $y = \frac{6}{7}x + \frac{5}{8}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -9x - 8

\newline

y = \frac{6}{7}x + \frac{5}{8}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = -9x - 8$ $\newline$ $y = \frac{6}{7}x + \frac{5}{8}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -9x - 8$ , the slope is $-9$ . $\newline$ In $y = \frac{6}{7}x + \frac{5}{8}$ , the slope is $\frac{6}{7}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine intersection point: Since the slopes of the two equations are different, this means that the lines they represent are not parallel and will intersect at exactly one point. This implies that the system of equations has a unique solution.
Classify system of equations: Choose the option which describes the given system of equations. $\newline$ Since the slopes are different and there is a unique solution, the system of equations is consistent and independent.

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