Which describes the system of equations below? y = –4/9x + 3 y = –4/9x + 7/3 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Analyze Slopes: Analyze the slopes of both equations. The first equation is y = –4/9x + 3, which has a slope of –4/9. The second equation is y = –4/9x + 7/3, which also has a slope of –4/9. 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 3. The y-intercept of the second equation is 7/3, which is also equal to 3 when converted to a mixed number (since 7/3 = 2 1/3 = 3). Since both y-intercepts are equal, the lines are the same line, and therefore, every point on one line is also on the other line.Determine System Type: Determine the type of system based on the slopes and y-intercepts. Since the slopes are equal and the y-intercepts are equal, the system of equations represents the same line. Therefore, the system has an infinite number of solutions, as any solution that works for one equation will also work for the other. This means the system is consistent (it has at least one solution) and dependent (the equations are dependent on each other, as they represent the same line).

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Which describes the system of equations below? $\newline$ $y = -\frac{4}{9}x + 3$ $\newline$ $y = -\frac{4}{9}x + \frac{7}{3}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (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{4}{9}x + 3

\newline

y = -\frac{4}{9}x + \frac{7}{3}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = \frac{-4}{9}x + 3$ , which has a slope of $\frac{-4}{9}$ . $\newline$ The second equation is $y = \frac{-4}{9}x + \frac{7}{3}$ , which also has a slope of $\frac{-4}{9}$ . $\newline$ 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 $3$ . $\newline$ The y-intercept of the second equation is $\frac{7}{3}$ , which is also equal to $3$ when converted to a mixed number (since $\frac{7}{3} = 2 \frac{1}{3} = 3$ ). $\newline$ Since both y-intercepts are equal, the lines are the same line, and therefore, every point on one line is also on the other line.
Determine System Type: Determine the type of system based on the slopes and $y$ -intercepts. $\newline$ Since the slopes are equal and the $y$ -intercepts are equal, the system of equations represents the same line. Therefore, the system has an infinite number of solutions, as any solution that works for one equation will also work for the other. $\newline$ This means the system is consistent (it has at least one solution) and dependent (the equations are dependent on each other, as they represent the same line).