Which describes the system of equations below? y = 7x − 3 y = 7x − 5/6 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Identify Slopes: We have the following system of equations: y = 7x − 3 y = 7x − 5/6 Identify whether the slopes of both the equations are the same. In y = 7x − 3, the slope is 7. In y = 7x − 5/6, the slope is also 7. Yes, the slopes of both equations are the same.Identify Y-Intercepts: Next, identify whether the y-intercepts of both equations are the same. In y = 7x − 3, the y-intercept is -3. In y = 7x − 5/6, the y-intercept is -5/6. No, the y-intercepts of both equations are not the same.Determine Intersection: Since the slopes of the equations are the same but the y-intercepts are different, the lines are parallel to each other and do not intersect. Choose the option which describes the given system of equations. The system of equations is inconsistent because they have no points in common.

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Which describes the system of equations below? $\newline$ $y = 7x - 3$ $\newline$ $y = 7x - \frac{5}{6}$ $\newline$ 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 = 7x - 3

\newline

y = 7x - \frac{5}{6}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Identify Slopes: We have the following system of equations: $\newline$ $y = 7x − 3$ $\newline$ $y = 7x − \frac{5}{6}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 7x − 3$ , the slope is $7$ . $\newline$ In $y = 7x − \frac{5}{6}$ , the slope is also $7$ . $\newline$ Yes, the slopes of both equations are the same.
Identify Y-Intercepts: Next, identify whether the y-intercepts of both equations are the same. $\newline$ In $y = 7x − 3$ , the y-intercept is $-3$ . $\newline$ In $y = 7x − \frac{5}{6}$ , the y-intercept is $-\frac{5}{6}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Determine Intersection: Since the slopes of the equations are the same but the y-intercepts are different, the lines are parallel to each other and do not intersect. $\newline$ Choose the option which describes the given system of equations. $\newline$ The system of equations is inconsistent because they have no points in common.