Which describes the system of equations below? y = 2x − 4 y = 2x − 3/4 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Analyze slopes: Analyze the slopes of both equations. The first equation is y = 2x − 4, which has a slope of 2. The second equation is y = 2x − 3/4, which also has a slope of 2. 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, y = 2x − 4, is -4. The y-intercept of the second equation, y = 2x − 3/4, is -3/4. Since the y-intercepts are different, the lines are not the same line.Determine system type: Determine the type of system based on the slopes and y-intercepts. Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect. Therefore, there are no solutions to this system of equations, and the system is inconsistent.

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Which describes the system of equations below? $\newline$ $y = 2x - 4$ $\newline$ $y = 2x - \frac{3}{4}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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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 = 2x - 4

\newline

y = 2x - \frac{3}{4}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Analyze slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = 2x − 4$ , which has a slope of $2$ . $\newline$ The second equation is $y = 2x − \frac{3}{4}$ , which also has a slope of $2$ . $\newline$ 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, $y = 2x − 4$ , is $-4$ . $\newline$ The y-intercept of the second equation, $y = 2x − \frac{3}{4}$ , is $-\frac{3}{4}$ . $\newline$ Since the y-intercepts are different, the lines are not the same line.
Determine system type: Determine the type of system based on the slopes and y-intercepts. $\newline$ Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect. $\newline$ Therefore, there are no solutions to this system of equations, and the system is inconsistent.