Which describes the system of equations below? y = 7x − 6 y = –4/5x + 2/9 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Analyze Equations: Analyze the given system of equations to determine its type. We have two equations: y = 7x − 6 (Equation 1) y = –4/5x + 2/9 (Equation 2) To determine if the system is consistent and independent, consistent and dependent, or inconsistent, we need to look at the slopes and y-intercepts of the two lines represented by these equations.Compare Slopes: Compare the slopes of the two lines. The slope of Equation 1 is 7, and the slope of Equation 2 is –4/5. Since the slopes are different, the lines are not parallel and therefore they must intersect at exactly one point.Determine Consistency: Determine if the system is consistent and independent, consistent and dependent, or inconsistent. Since the lines have different slopes and will intersect at exactly one point, the system is consistent and independent. This means there is one unique solution to the system.

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Which describes the system of equations below? $\newline$ $y = 7x - 6$ $\newline$ $y = -\frac{4}{5}x + \frac{2}{9}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent

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Grade 8

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 7x - 6

\newline

y = -\frac{4}{5}x + \frac{2}{9}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Analyze Equations: Analyze the given system of equations to determine its type. $\newline$ We have two equations: $\newline$ $y = 7x − 6$ (Equation $1$ ) $\newline$ $y = −\frac{4}{5}x + \frac{2}{9}$ (Equation $2$ ) $\newline$ To determine if the system is consistent and independent, consistent and dependent, or inconsistent, we need to look at the slopes and $y$ -intercepts of the two lines represented by these equations.
Compare Slopes: Compare the slopes of the two lines. $\newline$ The slope of Equation $1$ is $7$ , and the slope of Equation $2$ is $-\frac{4}{5}$ . Since the slopes are different, the lines are not parallel and therefore they must intersect at exactly one point.
Determine Consistency: Determine if the system is consistent and independent, consistent and dependent, or inconsistent. $\newline$ Since the lines have different slopes and will intersect at exactly one point, the system is consistent and independent. This means there is one unique solution to the system.