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Which describes the system of equations below? $\newline$ $y = 7x - 1$ $\newline$ $y = 7x + \frac{2}{5}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and independent $\newline$ (C)consistent and dependent

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Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 7x - 1

\newline

y = 7x + \frac{2}{5}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Identify slopes: We have the following system of equations: $\newline$ $y = 7x − 1$ $\newline$ $y = 7x + \frac{2}{5}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 7x − 1$ , the slope is $7$ . $\newline$ In $y = 7x + \frac{2}{5}$ , the slope is also $7$ . $\newline$ Yes, the slopes of both equations are the same.
Identify y-intercepts: Now, identify whether the y-intercepts of both equations are the same. $\newline$ In $y = 7x − 1$ , the y-intercept is $-1$ . $\newline$ In $y = 7x + \frac{2}{5}$ , the y-intercept is $\frac{2}{5}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Determine inconsistency: Since the slopes of the equations are the same but the $y$ -intercepts are different, the lines are parallel to each other and will never intersect. $\newline$ This means that there is no solution to the system of equations, and the system is inconsistent.

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