Which describes the system of equations below? y = 5x + 1 y = 5x + 1 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Compare slopes of equations: We have the system of equations: y = 5x + 1 y = 5x + 1 First, we need to compare the slopes of both equations. In y = 5x + 1, the slope is 5. In y = 5x + 1, the slope is also 5.Compare y-intercepts: Next, we compare the y-intercepts of both equations. In y = 5x + 1, the y-intercept is 1. In y = 5x + 1, the y-intercept is also 1.Identify identical lines: Since both the slope and y-intercept of the two equations are the same, the lines they represent are identical. This means every solution to one equation is also a solution to the other, and they have infinitely many points in common.Determine consistency and dependency: Choose the option which describes the given system of equations. Since the slopes and y-intercepts are the same, the system of equations is consistent and dependent.

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Which describes the system of equations below? $\newline$ $y = 5x + 1$ $\newline$ $y = 5x + 1$ $\newline$ Choices: $\newline$ (A) inconsistent $\newline$ (B) consistent and independent $\newline$ (C) consistent and dependent

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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 + 1

\newline

y = 5x + 1

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and independent

\newline

Compare slopes of equations: We have the system of equations: $\newline$ $y = 5x + 1$ $\newline$ $y = 5x + 1$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = 5x + 1$ , the slope is $5$ . $\newline$ In $y = 5x + 1$ , the slope is also $5$ .
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = 5x + 1$ , the y-intercept is $1$ . $\newline$ In $y = 5x + 1$ , the y-intercept is also $1$ .
Identify identical lines: Since both the slope and $y$ -intercept of the two equations are the same, the lines they represent are identical. This means every solution to one equation is also a solution to the other, and they have infinitely many points in common.
Determine consistency and dependency: Choose the option which describes the given system of equations. Since the slopes and $y$ -intercepts are the same, the system of equations is consistent and dependent.