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

Identify Slopes: Identify the slopes of the given equations to determine if they are parallel, the same, or intersecting. For the first equation, y = –7x − 2, the slope (m1) is –7. For the second equation, y = 2/5x − 2/7, the slope (m2) is 2/5. Check if m1 equals m2. Compare Slopes: Compare the slopes. Since –7 is not equal to 2/5, the lines are not parallel and not the same line. This means they must intersect at exactly one point. Determine System Type: Determine the type of system based on the slopes. Since the lines intersect at exactly one point, the system is consistent and independent.

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

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Math Problems

Grade 8

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -7x - 2

\newline

y = \frac{2}{5}x - \frac{2}{7}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

Identify Slopes: Identify the slopes of the given equations to determine if they are parallel, the same, or intersecting. $\newline$ For the first equation, $y = -7x - 2$ , the slope ( $m_1$ ) is $-7$ . $\newline$ For the second equation, $y = \frac{2}{5}x - \frac{2}{7}$ , the slope ( $m_2$ ) is $\frac{2}{5}$ . $\newline$ Check if $m_1$ equals $m_2$ .
Compare Slopes: Compare the slopes. $\newline$ Since $-7$ is not equal to $\frac{2}{5}$ , the lines are not parallel and not the same line. $\newline$ This means they must intersect at exactly one point.
Determine System Type: Determine the type of system based on the slopes. $\newline$ Since the lines intersect at exactly one point, the system is consistent and independent.