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

Compare Slopes: We have the following system of equations: y = (9/5)x - 5 y = (9/5)x + 8/9 First, we need to compare the slopes of both equations to determine if they are parallel, the same line, or intersecting lines. The slope of the first equation is 9/5. The slope of the second equation is also 9/5. Since both slopes are equal, the lines are either the same line (consistent and dependent) or parallel lines (inconsistent).Compare Y-Intercepts: Next, we need to compare the y-intercepts of both equations to determine if they are the same line or parallel lines. The y-intercept of the first equation is -5. The y-intercept of the second equation is 8/9. Since the y-intercepts are different, the lines are not the same line. Therefore, the lines are parallel and do not intersect.Determine Intersection: Since the lines have the same slope but different y-intercepts, they will never intersect. This means the system of equations has no solution. The correct description of the system is that it is inconsistent.

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

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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 = \frac{9}{5}x - 5

\newline

y = \frac{9}{5}x + \frac{8}{9}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

\newline

Compare Slopes: We have the following system of equations: $\newline$ $y = \frac{9}{5}x - 5$ $\newline$ $y = \frac{9}{5}x + \frac{8}{9}$ $\newline$ First, we need to compare the slopes of both equations to determine if they are parallel, the same line, or intersecting lines. $\newline$ The slope of the first equation is $\frac{9}{5}$ . $\newline$ The slope of the second equation is also $\frac{9}{5}$ . $\newline$ Since both slopes are equal, the lines are either the same line (consistent and dependent) or parallel lines (inconsistent).
Compare Y-Intercepts: Next, we need to compare the $y$ -intercepts of both equations to determine if they are the same line or parallel lines. $\newline$ The $y$ -intercept of the first equation is $-5$ . $\newline$ The $y$ -intercept of the second equation is $\frac{8}{9}$ . $\newline$ Since the $y$ -intercepts are different, the lines are not the same line. $\newline$ Therefore, the lines are parallel and do not intersect.
Determine Intersection: Since the lines have the same slope but different $y$ -intercepts, they will never intersect. This means the system of equations has no solution. $\newline$ The correct description of the system is that it is inconsistent.