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Which describes the system of equations below? $\newline$ $y = 2x - 8$ $\newline$ $y = 2x - 8$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = 2x - 8

\newline

y = 2x - 8

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Compare slopes: We have the system of equations: $\newline$ $y = 2x - 8$ $\newline$ $y = 2x - 8$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = 2x - 8$ , the slope is $2$ . $\newline$ In $y = 2x - 8$ , the slope is also $2$ .
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = 2x - 8$ , the y-intercept is $-8$ . $\newline$ In $y = 2x - 8$ , the y-intercept is also $-8$ .
Identical lines: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are identical. This means that every solution to one equation is also a solution to the other, and there are infinitely many solutions.
Consistent and dependent: Choose the option which describes the given system of equations. $\newline$ Since the slopes and $y$ -intercepts are the same, the system of equations is consistent and dependent. This means that the two equations represent the same line, and they have all their points in common.

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