Which describes the system of equations below? y = –6x − 8 y = –6x − 8 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Equations Given: We have the system of equations: y = –6x − 8 y = –6x − 8 First, we need to compare the slopes of both equations. In y = –6x − 8, the slope is -6. In y = –6x − 8, the slope is also -6.Compare Slopes: Next, we compare the y-intercepts of both equations. In y = –6x − 8, the y-intercept is -8. In y = –6x − 8, the y-intercept is also -8.Compare Y-Intercepts: Since both the slope and y-intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, every solution to one equation is also a solution to the other, which means the system has an infinite number of solutions.Identical Lines: Choose the option that correctly describes the system of equations. Since the lines are identical and have an infinite number of solutions, the system is consistent (because there are solutions) and dependent (because the equations represent the same line).

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Which describes the system of equations below? $\newline$ $y = -6x - 8$ $\newline$ $y = -6x - 8$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent

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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 = -6x - 8

\newline

y = -6x - 8

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Equations Given: We have the system of equations: $\newline$ $y = -6x - 8$ $\newline$ $y = -6x - 8$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -6x - 8$ , the slope is $-6$ . $\newline$ In $y = -6x - 8$ , the slope is also $-6$ .
Compare Slopes: Next, we compare the $y$ -intercepts of both equations. $\newline$ In $y = -6x - 8$ , the $y$ -intercept is $-8$ . $\newline$ In $y = -6x - 8$ , the $y$ -intercept is also $-8$ .
Compare Y-Intercepts: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, every solution to one equation is also a solution to the other, which means the system has an infinite number of solutions.
Identical Lines: Choose the option that correctly describes the system of equations. Since the lines are identical and have an infinite number of solutions, the system is consistent (because there are solutions) and dependent (because the equations represent the same line).