Which describes the system of equations below? y = –9/5x + 2 y = –9/5x + 3/2 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. The first equation is y = –9/5x + 2, which has a slope of –9/5. The second equation is y = –9/5x + 3/2, which also has a slope of –9/5. Since both slopes are equal, the lines are either the same line (if they have the same y-intercept) or parallel lines (if they have different y-intercepts).Compare y-intercepts: Compare the y-intercepts of both equations. The y-intercept of the first equation is 2. The y-intercept of the second equation is 3/2. Since the y-intercepts are different, the lines are parallel and do not intersect.Determine system type: Determine the type of system based on the slopes and y-intercepts. Since the lines have the same slope but different y-intercepts, they will never intersect. This means there are no solutions to the system of equations. The system is therefore inconsistent.

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Which describes the system of equations below? $\newline$ $y = -\frac{9}{5}x + 2$ $\newline$ $y = -\frac{9}{5}x + \frac{3}{2}$ $\newline$ 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 = -\frac{9}{5}x + 2

\newline

y = -\frac{9}{5}x + \frac{3}{2}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ The first equation is $y = -\frac{9}{5}x + 2$ , which has a slope of $-\frac{9}{5}$ . $\newline$ The second equation is $y = -\frac{9}{5}x + \frac{3}{2}$ , which also has a slope of $-\frac{9}{5}$ . $\newline$ Since both slopes are equal, the lines are either the same line (if they have the same $y$ -intercept) or parallel lines (if they have different $y$ -intercepts).
Compare y-intercepts: Compare the y-intercepts of both equations. $\newline$ The y-intercept of the first equation is $2$ . $\newline$ The y-intercept of the second equation is $\frac{3}{2}$ . $\newline$ Since the y-intercepts are different, the lines are parallel and do not intersect.
Determine system type: Determine the type of system based on the slopes and $y$ -intercepts. $\newline$ Since the lines have the same slope but different $y$ -intercepts, they will never intersect. This means there are no solutions to the system of equations. $\newline$ The system is therefore inconsistent.