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Which describes the system of equations below? $\newline$ $y = 6x + 1$ $\newline$ $y = 6x + 1$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = 6x + 1

\newline

y = 6x + 1

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Compare Slopes: We have the system of equations: $\newline$ $y = 6x + 1$ $\newline$ $y = 6x + 1$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = 6x + 1$ , the slope is $6$ . $\newline$ In $y = 6x + 1$ , the slope is also $6$ .
Compare Y-Intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = 6x + 1$ , the y-intercept is $1$ . $\newline$ In $y = 6x + 1$ , the y-intercept is also $1$ .
Identical Lines: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are identical. This means that every solution to one equation is also a solution to the other, and there are infinitely many solutions.
Consistent and Dependent: Therefore, the system of equations is consistent because there are solutions, and it is dependent because the equations represent the same line and thus have all their solutions in common.

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