Which describes the system of equations below? y = –5x − 10 y = –5x − 10 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Equations and Slopes: We have the system of equations: y = –5x − 10 y = –5x − 10 First, we need to compare the slopes of both equations. In y = –5x − 10, the slope is –5. In y = –5x − 10, the slope is also –5. Since both slopes are the same, we can say that the lines are either parallel or the same line.Y-Intercepts Comparison: Next, we compare the y-intercepts of both equations. In y = –5x − 10, the y-intercept is –10. In y = –5x − 10, the y-intercept is also –10. Since both y-intercepts are the same, we can conclude that the lines are not just parallel, but they are in fact the same line.Consistency and Dependence: Since both the slope and y-intercept of the two equations are the same, the system of equations represents the same line. Therefore, any solution that lies on one line will also lie on the other, meaning there are infinitely many solutions. This means the system of equations is consistent because there are solutions, and it is dependent because the equations describe the same line and thus have all their solutions in common.

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Which describes the system of equations below? $\newline$ $y = -5x - 10$ $\newline$ $y = -5x - 10$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -5x - 10

\newline

y = -5x - 10

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Equations and Slopes: We have the system of equations: $\newline$ $y = -5x - 10$ $\newline$ $y = -5x - 10$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -5x - 10$ , the slope is $-5$ . $\newline$ In $y = -5x - 10$ , the slope is also $-5$ . $\newline$ Since both slopes are the same, we can say that the lines are either parallel or the same line.
Y-Intercepts Comparison: Next, we compare the y-intercepts of both equations. $\newline$ In $y = -5x - 10$ , the y-intercept is $-10$ . $\newline$ In $y = -5x - 10$ , the y-intercept is also $-10$ . $\newline$ Since both y-intercepts are the same, we can conclude that the lines are not just parallel, but they are in fact the same line.
Consistency and Dependence: Since both the slope and $y$ -intercept of the two equations are the same, the system of equations represents the same line. Therefore, any solution that lies on one line will also lie on the other, meaning there are infinitely many solutions. $\newline$ This means the system of equations is consistent because there are solutions, and it is dependent because the equations describe the same line and thus have all their solutions in common.