"Which describes the system of equations below? y = –3x + 9 y = –3x + 9 Choices: [[consistent and independent][consistent and dependent][inconsistent]] "

Given Equations: We are given two equations: y = –3x + 9 y = –3x + 9 We need to determine if they are consistent and independent, consistent and dependent, or inconsistent. First, let's compare the slopes of both equations. The slope of the first equation is -3, and the slope of the second equation is also -3.Comparison of Slopes: Next, let's compare the y-intercepts of both equations. The y-intercept of the first equation is 9, and the y-intercept of the second equation is also 9.Comparison of Y-Intercepts: 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.Consistency and Dependence: 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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Which describes the system of equations below? $\newline$ $y = –3x + 9$ $\newline$ $y = –3x + 9$ $\newline$ Choices: $\newline$ $\text{(A) consistent and independent}$ $\newline$ $\text{(B) consistent and dependent}$ $\newline$ $\text{(C) inconsistent}$

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Algebra 2

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = –3x + 9

\newline

y = –3x + 9

\newline

Choices:

\newline

\text{(A) consistent and independent}

\newline

\text{(B) consistent and dependent}

\newline

\text{(C) inconsistent}

Given Equations: We are given two equations: $\newline$ $y = -3x + 9$ $\newline$ $y = -3x + 9$ $\newline$ We need to determine if they are consistent and independent, consistent and dependent, or inconsistent. $\newline$ First, let's compare the slopes of both equations. $\newline$ The slope of the first equation is $-3$ , and the slope of the second equation is also $-3$ .
Comparison of Slopes: Next, let's compare the y-intercepts of both equations. The y-intercept of the first equation is $9$ , and the y-intercept of the second equation is also $9$ .
Comparison of Y-Intercepts: 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.
Consistency and Dependence: 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.