Which describes the system of equations below? y = –6x − 7/5 y = 1/6x + 2/3 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify slopes of equations: We have the system of equations: y = –6x – 7/5 y = 1/6x + 2/3 Identify whether the slopes of both the equations are the same. In y = –6x – 7/5, the slope is –6. In y = 1/6x + 2/3, the slope is 1/6. No, the slopes of both the equations are not the same.Determine intersection of lines: Since the slopes are different, the lines represented by these equations are not parallel and will intersect at exactly one point. This means the system of equations has one solution where the two lines intersect.Check consistency and independence: Choose the option which describes the given system of equations. Since the slopes are different and the lines intersect at one point, the system of equations is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = -6x - \frac{7}{5}$ $\newline$ $y = \frac{1}{6}x + \frac{2}{3}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (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 = -6x - \frac{7}{5}

\newline

y = \frac{1}{6}x + \frac{2}{3}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify slopes of equations: We have the system of equations: $\newline$ $y = -6x - \frac{7}{5}$ $\newline$ $y = \frac{1}{6}x + \frac{2}{3}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -6x - \frac{7}{5}$ , the slope is $-6$ . $\newline$ In $y = \frac{1}{6}x + \frac{2}{3}$ , the slope is $\frac{1}{6}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine intersection of lines: Since the slopes are different, the lines represented by these equations are not parallel and will intersect at exactly one point. This means the system of equations has one solution where the two lines intersect.
Check consistency and independence: Choose the option which describes the given system of equations. $\newline$ Since the slopes are different and the lines intersect at one point, the system of equations is consistent and independent.