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

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -8x - 9

\newline

y = -8x - 9

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Compare Slopes: We have the system of equations: $\newline$ $y = -8x - 9$ $\newline$ $y = -8x - 9$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -8x - 9$ , the slope is $-8$ . $\newline$ In $y = -8x - 9$ , the slope is also $-8$ . $\newline$ Since both slopes are the same, 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 $y = -8x - 9$ , the y-intercept is $-9$ . $\newline$ In $y = -8x - 9$ , the y-intercept is also $-9$ . $\newline$ Since both y-intercepts are the same, we can conclude that both equations represent the same line.
Conclusion: Since both the slope and $y$ -intercept of the two equations are identical, the system of equations represents the same line. Therefore, the system has an infinite number of solutions where the two equations intersect, which means the system is consistent and dependent.

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