Which describes the system of equations below? y = –10x − 1 y = –10x − 1 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Equations Comparison: We have the system of equations: y = –10x − 1 y = –10x − 1 First, we need to compare the slopes of both equations. In y = –10x − 1, the slope is –10. In y = –10x − 1, the slope is also –10. Since both slopes are the same, we can say that the lines are parallel or the same line.Slope Comparison: Next, we compare the y-intercepts of both equations. In y = –10x − 1, the y-intercept is –1. In y = –10x − 1, the y-intercept is also –1. Since both y-intercepts are the same, we can conclude that the equations represent the same line.Y-Intercept Comparison: 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 satisfies one equation will also satisfy the other. This means that the system has an infinite number of solutions, and the equations are dependent on each other.Conclusion: Choose the option which describes the given system of equations. Since the system has an infinite number of solutions and the equations are dependent on each other, the correct choice is: (A) consistent and dependent.

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Which describes the system of equations below? $\newline$ $y = -10x - 1$ $\newline$ $y = -10x - 1$ $\newline$ 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 = -10x - 1

\newline

y = -10x - 1

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Equations Comparison: We have the system of equations: $\newline$ $y = -10x - 1$ $\newline$ $y = -10x - 1$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -10x - 1$ , the slope is $-10$ . $\newline$ In $y = -10x - 1$ , the slope is also $-10$ . $\newline$ Since both slopes are the same, we can say that the lines are parallel or the same line.
Slope Comparison: Next, we compare the y-intercepts of both equations. $\newline$ In $y = -10x - 1$ , the y-intercept is $-1$ . $\newline$ In $y = -10x - 1$ , the y-intercept is also $-1$ . $\newline$ Since both y-intercepts are the same, we can conclude that the equations represent the same line.
Y-Intercept Comparison: 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 satisfies one equation will also satisfy the other. $\newline$ This means that the system has an infinite number of solutions, and the equations are dependent on each other.
Conclusion: Choose the option which describes the given system of equations. $\newline$ Since the system has an infinite number of solutions and the equations are dependent on each other, the correct choice is: $\newline$ (A) consistent and dependent.