Which describes the system of equations below? y = –10x + 4 y = –10x + 4 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Compare slopes: We have the system of equations: y = –10x + 4 y = –10x + 4 First, we need to compare the slopes of both equations. In y = –10x + 4, the slope is -10. In y = –10x + 4, the slope is also -10.Compare y-intercepts: Next, we compare the y-intercepts of both equations. In y = –10x + 4, the y-intercept is 4. In y = –10x + 4, the y-intercept is also 4.Identify 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.Determine consistency: Choose the option which describes the given system of equations. Since the slopes and y-intercepts are the same, and the lines are identical, the system of equations is consistent and dependent.

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Which describes the system of equations below? $\newline$ $y = -10x + 4$ $\newline$ $y = -10x + 4$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent

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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 = -10x + 4

\newline

y = -10x + 4

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Compare slopes: We have the system of equations: $\newline$ $y = -10x + 4$ $\newline$ $y = -10x + 4$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -10x + 4$ , the slope is $-10$ . $\newline$ In $y = -10x + 4$ , the slope is also $-10$ .
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = -10x + 4$ , the y-intercept is $4$ . $\newline$ In $y = -10x + 4$ , the y-intercept is also $4$ .
Identify 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.
Determine consistency: Choose the option which describes the given system of equations. Since the slopes and $y$ -intercepts are the same, and the lines are identical, the system of equations is consistent and dependent.