Which describes the system of equations below? y = 6x + 8 y = –4/5x + 7/5 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Identify Slopes: We have the system of equations: y = 6x + 8 y = -4/5x + 7/5 Identify whether the slopes of both the equations are the same. In y = 6x + 8, the slope is 6. In y = -4/5x + 7/5, the slope is -4/5. No, the slopes of both the equations are not the same.Determine Unique Solution: Since the slopes of the two equations are different, this means that the lines will intersect at exactly one point. This implies that the system of equations has a unique solution.Choose System Description: Choose the option which describes the given system of equations. Since the slopes are different and there is a unique solution, the system of equations is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = 6x + 8$ $\newline$ $y = -\frac{4}{5}x + \frac{7}{5}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent

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Math Problems

Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 6x + 8

\newline

y = -\frac{4}{5}x + \frac{7}{5}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Identify Slopes: We have the system of equations: $\newline$ $y = 6x + 8$ $\newline$ $y = -\frac{4}{5}x + \frac{7}{5}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 6x + 8$ , the slope is $6$ . $\newline$ In $y = -\frac{4}{5}x + \frac{7}{5}$ , the slope is $-\frac{4}{5}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine Unique Solution: Since the slopes of the two equations are different, this means that the lines will intersect at exactly one point. This implies that the system of equations has a unique solution.
Choose System Description: Choose the option which describes the given system of equations. $\newline$ Since the slopes are different and there is a unique solution, the system of equations is consistent and independent.