Which describes the system of equations below? y = 2/5x − 10/7 y = –4/5x − 10/7 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Identify slopes: We have the system of equations: y = (2/5)x - 10/7 y = (-4/5)x - 10/7 Identify whether the slopes of both the equations are the same. In y = (2/5)x - 10/7, the slope is 2/5. In y = (-4/5)x - 10/7, the slope is -4/5. No, the slopes of both the equations are not the same. Check for parallel lines: 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 and independent.

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Which describes the system of equations below? $\newline$ $y = \frac{2}{5}x - \frac{10}{7}$ $\newline$ $y = -\frac{4}{5}x - \frac{10}{7}$ $\newline$ 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 = \frac{2}{5}x - \frac{10}{7}

\newline

y = -\frac{4}{5}x - \frac{10}{7}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Identify slopes: We have the system of equations: $\newline$ $y = \frac{2}{5}x - \frac{10}{7}$ $\newline$ $y = \frac{-4}{5}x - \frac{10}{7}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = \frac{2}{5}x - \frac{10}{7}$ , the slope is $\frac{2}{5}$ . $\newline$ In $y = \frac{-4}{5}x - \frac{10}{7}$ , the slope is $\frac{-4}{5}$ . $\newline$ No, the slopes of both the equations are not the same.
Check for parallel lines: 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 and independent.