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

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{5}{2}x - 3

\newline

y = \frac{5}{2}x - 3

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Compare slopes: We have the system of equations: $\newline$ y = $(\frac{5}{2})x - 3$ $\newline$ y = $(\frac{5}{2})x - 3$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = (\frac{5}{2})x - 3$ , the slope is $\frac{5}{2}$ . $\newline$ In $y = (\frac{5}{2})x - 3$ , the slope is also $\frac{5}{2}$ . $\newline$ Since both slopes are equal, we can say that the lines are either the same line (consistent and dependent) or parallel lines (inconsistent).
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = \frac{5}{2}x - 3$ , the y-intercept is $-3$ . $\newline$ In $y = \frac{5}{2}x - 3$ , the y-intercept is also $-3$ . $\newline$ Since both y-intercepts are equal, we can conclude that the two equations represent the same line. Therefore, the system of equations is consistent and dependent.

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