Which describes the system of equations below? y = –7x + 4 y = –7x + 4 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Compare slopes and intercepts: We are given the system of equations: y = –7x + 4 y = –7x + 4 First, we need to compare the slopes and y-intercepts of both equations to determine the nature of the system.Identify same line: The slope of the first equation y = –7x + 4 is -7, and the y-intercept is 4. The slope of the second equation y = –7x + 4 is also -7, and the y-intercept is also 4.Infinite solutions: Since both equations have the same slope and y-intercept, they represent the same line. Therefore, every solution to one equation is also a solution to the other, which means the system has an infinite number of solutions.Consistent and dependent: A system with an infinite number of solutions is considered consistent because there are solutions, and dependent because the equations are essentially the same, so they depend on each other for the solutions.

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Which describes the system of equations below? $\newline$ $y = -7x + 4$ $\newline$ $y = -7x + 4$ $\newline$ 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 = -7x + 4

\newline

y = -7x + 4

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and independent

\newline

Compare slopes and intercepts: We are given the system of equations: $\newline$ $y = -7x + 4$ $\newline$ $y = -7x + 4$ $\newline$ First, we need to compare the slopes and $y$ -intercepts of both equations to determine the nature of the system.
Identify same line: The slope of the first equation $y = -7x + 4$ is $-7$ , and the y-intercept is $4$ . The slope of the second equation $y = -7x + 4$ is also $-7$ , and the y-intercept is also $4$ .
Infinite solutions: Since both equations have the same slope and $y$ -intercept, they represent the same line. Therefore, every solution to one equation is also a solution to the other, which means the system has an infinite number of solutions.
Consistent and dependent: A system with an infinite number of solutions is considered consistent because there are solutions, and dependent because the equations are essentially the same, so they depend on each other for the solutions.