Which describes the system of equations below? y = 6x − 2 y = 1/5x − 7/4 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify slopes of equations: We have the following system of equations: y = 6x − 2 y = (1/5)x − 7/4 Identify whether the slopes of both the equations are the same. In y = 6x − 2, the slope is 6. In y = (1/5)x − 7/4, the slope is 1/5. Since 6 is not equal to 1/5, the slopes of both equations are different.Comparison of slopes: Since the slopes of the two equations are different, the lines they represent are not parallel. This means they will intersect at some point. Therefore, the system of equations has a unique solution where the two lines intersect. This makes the system consistent and independent.

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Which describes the system of equations below? $\newline$ $y = 6x - 2$ $\newline$ $y = \frac{1}{5}x - \frac{7}{4}$ $\newline$ 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 - 2

\newline

y = \frac{1}{5}x - \frac{7}{4}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = 6x − 2$ $\newline$ $y = \frac{1}{5}x − \frac{7}{4}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 6x − 2$ , the slope is $6$ . $\newline$ In $y = \frac{1}{5}x − \frac{7}{4}$ , the slope is $\frac{1}{5}$ . $\newline$ Since $6$ is not equal to $\frac{1}{5}$ , the slopes of both equations are different.
Comparison of slopes: Since the slopes of the two equations are different, the lines they represent are not parallel. This means they will intersect at some point. $\newline$ Therefore, the system of equations has a unique solution where the two lines intersect. $\newline$ This makes the system consistent and independent.