Which describes the system of equations below? y = 1/9x − 3 y = 1/9x − 3 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Equations and Slopes: We have the system of equations: y = (1/9)x - 3 y = (1/9)x - 3 First, we need to compare the slopes of both equations. In y = (1/9)x - 3, the slope is 1/9. In y = (1/9)x - 3, the slope is also 1/9. Since the slopes are the same, we can say that the lines are parallel or coincident.Y-Intercepts Comparison: Next, we compare the y-intercepts of both equations. In y = (1/9)x - 3, the y-intercept is -3. In y = (1/9)x - 3, the y-intercept is also -3. Since the y-intercepts are the same, we can say that the lines are coincident, meaning they lie on top of each other.Conclusion: Since both the slope and y-intercept of the two equations are the same, the lines represented by these equations are the same line. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. The system of equations is consistent because there are solutions, and it is dependent because the equations represent the same line.

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Which describes the system of equations below? $\newline$ $y = \frac{1}{9}x - 3$ $\newline$ $y = \frac{1}{9}x - 3$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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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{1}{9}x - 3

\newline

y = \frac{1}{9}x - 3

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Equations and Slopes: We have the system of equations: $\newline$ $y = \frac{1}{9}x - 3$ $\newline$ $y = \frac{1}{9}x - 3$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = \frac{1}{9}x - 3$ , the slope is $\frac{1}{9}$ . $\newline$ In $y = \frac{1}{9}x - 3$ , the slope is also $\frac{1}{9}$ . $\newline$ Since the slopes are the same, we can say that the lines are parallel or coincident.
Y-Intercepts Comparison: Next, we compare the y-intercepts of both equations. $\newline$ In $y = \frac{1}{9}x - 3$ , the y-intercept is $-3$ . $\newline$ In $y = \frac{1}{9}x - 3$ , the y-intercept is also $-3$ . $\newline$ Since the y-intercepts are the same, we can say that the lines are coincident, meaning they lie on top of each other.
Conclusion: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are the same line. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. $\newline$ The system of equations is consistent because there are solutions, and it is dependent because the equations represent the same line.