Which describes the system of equations below? y = –8x + 8 y = –9/5x + 9/4 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Analyze System Type: Analyze the given system of equations to determine its type. We have two equations: y = –8x + 8 (Equation 1) y = –9/5x + 9/4 (Equation 2) To determine if the system is consistent and dependent, consistent and independent, or inconsistent, we need to compare the slopes and y-intercepts of the two lines represented by these equations.Compare Slopes: Compare the slopes of the two equations. The slope of Equation 1 is -8. The slope of Equation 2 is -9/5. Since the slopes are different (-8 ≠ -9/5), the lines are not parallel and therefore they are not consistent and dependent.Determine Consistency: Determine if the system is inconsistent or consistent and independent. Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent and independent.

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Which describes the system of equations below? $\newline$ $y = -8x + 8$ $\newline$ $y = -\frac{9}{5}x + \frac{9}{4}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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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 = -8x + 8

\newline

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

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Analyze System Type: Analyze the given system of equations to determine its type. $\newline$ We have two equations: $\newline$ $y = -8x + 8$ (Equation $1$ ) $\newline$ $y = -\frac{9}{5}x + \frac{9}{4}$ (Equation $2$ ) $\newline$ To determine if the system is consistent and dependent, consistent and independent, or inconsistent, we need to compare the slopes and y-intercepts of the two lines represented by these equations.
Compare Slopes: Compare the slopes of the two equations. $\newline$ The slope of Equation $1$ is $-8$ . $\newline$ The slope of Equation $2$ is $-\frac{9}{5}$ . $\newline$ Since the slopes are different ( $-8 \neq -\frac{9}{5}$ ), the lines are not parallel and therefore they are not consistent and dependent.
Determine Consistency: Determine if the system is inconsistent or consistent and independent. $\newline$ Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent and independent.