Which describes the system of equations below? y = –6x + 5 y = –8/9x + 7/8 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Identify slopes of equations: We have the following system of equations: y = –6x + 5 y = –8/9x + 7/8 Identify whether the slopes of both the equations are the same. In y = –6x + 5, the slope is –6. In y = –8/9x + 7/8, the slope is –8/9. No, the slopes of both the equations are not the same.Determine if slopes are same: Since the slopes are different, the lines are not parallel and will intersect at some point. This means that there is one solution to the system of equations. Therefore, the system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution.

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Which describes the system of equations below? $\newline$ $y = -6x + 5$ $\newline$ $y = -\frac{8}{9}x + \frac{7}{8}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (C)consistent and independent

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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 = -6x + 5

\newline

y = -\frac{8}{9}x + \frac{7}{8}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = -6x + 5$ $\newline$ $y = -\frac{8}{9}x + \frac{7}{8}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -6x + 5$ , the slope is $-6$ . $\newline$ In $y = -\frac{8}{9}x + \frac{7}{8}$ , the slope is $-\frac{8}{9}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine if slopes are same: Since the slopes are different, the lines are not parallel and will intersect at some point. This means that there is one solution to the system of equations. Therefore, the system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution.