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Which describes the system of equations below? $\newline$ $y = \frac{4}{3}x + 6$ $\newline$ $y = \frac{9}{5}x + \frac{9}{8}$ $\newline$ 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 = \frac{4}{3}x + 6

\newline

y = \frac{9}{5}x + \frac{9}{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: $\newline$ $y = \frac{4}{3}x + 6$ $\newline$ $y = \frac{9}{5}x + \frac{9}{8}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = \frac{4}{3}x + 6$ , the slope is $\frac{4}{3}$ . $\newline$ In $y = \frac{9}{5}x + \frac{9}{8}$ , the slope is $\frac{9}{5}$ . $\newline$ Since $\frac{4}{3}$ is not equal to $\frac{9}{5}$ , the slopes of both equations are different.
Determine if slopes are same: Since the slopes are different, 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 unique solution. Therefore, the system of equations is consistent and independent.

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