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Which describes the system of equations below? $\newline$ $y = \frac{1}{8}x + 10$ $\newline$ $y = \frac{1}{8}x + 10$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{1}{8}x + 10

\newline

y = \frac{1}{8}x + 10

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Check Slopes: Step $1$ : Check if the slopes of both equations are the same. $\newline$ In $y = \frac{1}{8}x + 10$ , the slope is $\frac{1}{8}$ . $\newline$ In $y = \frac{1}{8}x + 10$ , the slope is also $\frac{1}{8}$ .
Check Y-Intercepts: Step $2$ : Check if the y-intercepts of both equations are the same. $\newline$ In $y = \frac{1}{8}x + 10$ , the y-intercept is $10$ . $\newline$ In $y = \frac{1}{8}x + 10$ , the y-intercept is also $10$ .
Determine System Type: Step $3$ : Determine the type of system based on the slopes and $y$ -intercepts. $\newline$ Since both the slope and $y$ -intercept are the same for both equations, the lines are identical. This means every solution of one equation is a solution of the other, so the system is consistent and dependent.

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