Which describes the system of equations below? y = –2x + 6 y = –2x + 6 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Compare Slopes: We have the system of equations: y = –2x + 6 y = –2x + 6 First, we need to compare the slopes of both equations. In y = –2x + 6, the slope is -2. In y = –2x + 6, the slope is also -2.Compare Y-Intercepts: Next, we compare the y-intercepts of both equations. In y = –2x + 6, the y-intercept is 6. In y = –2x + 6, the y-intercept is also 6.Identical Lines: Since both the slope and y-intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions.Consistent and Dependent: Choose the option that correctly describes the system of equations. Since the lines are identical, the system is consistent because there are solutions, and it is dependent because the equations represent the same line.

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Which describes the system of equations below? $\newline$ $y = -2x + 6$ $\newline$ $y = -2x + 6$ $\newline$ Choices: $\newline$ (A) inconsistent $\newline$ (B) consistent and independent $\newline$ (C) consistent and dependent

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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 = -2x + 6

\newline

y = -2x + 6

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and independent

\newline

Compare Slopes: We have the system of equations: $\newline$ $y = -2x + 6$ $\newline$ $y = -2x + 6$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = -2x + 6$ , the slope is $-2$ . $\newline$ In $y = -2x + 6$ , the slope is also $-2$ .
Compare Y-Intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = -2x + 6$ , the y-intercept is $6$ . $\newline$ In $y = -2x + 6$ , the y-intercept is also $6$ .
Identical Lines: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions.
Consistent and Dependent: Choose the option that correctly describes the system of equations. Since the lines are identical, the system is consistent because there are solutions, and it is dependent because the equations represent the same line.