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Which describes the system of equations below? $\newline$ $y = -3x - 6$ $\newline$ $y = -3x - 6$ $\newline$ 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 = -3x - 6

\newline

y = -3x - 6

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Equations Comparison: We have the system of equations: $\newline$ $y = -3x - 6$ $\newline$ $y = -3x - 6$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -3x - 6$ , the slope is $-3$ . $\newline$ In $y = -3x - 6$ , the slope is also $-3$ .
Slope and Y-Intercept Comparison: Next, we compare the y-intercepts of both equations. $\newline$ In $y = -3x - 6$ , the y-intercept is $-6$ . $\newline$ In $y = -3x - 6$ , the y-intercept is also $-6$ .
Conclusion: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. $\newline$ The system of equations is consistent because there are solutions, and it is dependent because the equations represent the same line.

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