Which describes the system of equations below? y = 3/8x + 7/4 y = 3/8x − 2/9 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Identify slopes and y-intercepts: Analyze the equations to identify their slopes and y-intercepts. Equation 1: y = 3/8x + 7/4 Equation 2: y = 3/8x - 2/9 Both equations have the same slope (3/8), but different y-intercepts (7/4 and -2/9). Determine relationship based on slopes and y-intercepts: Determine the relationship between the equations based on their slopes and y-intercepts. Since the slopes are identical but the y-intercepts are different, the lines are parallel and never intersect. Conclude system type: Conclude the type of system they form. Parallel lines with the same slope and different y-intercepts mean the system is inconsistent; there are no points of intersection.

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Which describes the system of equations below? $\newline$ $y = \frac{3}{8}x + \frac{7}{4}$ $\newline$ $y = \frac{3}{8}x - \frac{2}{9}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent $\newline$

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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 = \frac{3}{8}x + \frac{7}{4}

\newline

y = \frac{3}{8}x - \frac{2}{9}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

\newline

Identify slopes and y-intercepts: Analyze the equations to identify their slopes and y-intercepts. $\newline$ Equation $1$ : $y = \frac{3}{8}x + \frac{7}{4}$ $\newline$ Equation $2$ : $y = \frac{3}{8}x - \frac{2}{9}$ $\newline$ Both equations have the same slope ( $\frac{3}{8}$ ), but different y-intercepts ( $\frac{7}{4}$ and $-\frac{2}{9}$ ).
Determine relationship based on slopes and y-intercepts: Determine the relationship between the equations based on their slopes and y-intercepts. $\newline$ Since the slopes are identical but the y-intercepts are different, the lines are parallel and never intersect.
Conclude system type: Conclude the type of system they form. Parallel lines with the same slope $m$ and different $y$ -intercepts mean the system is inconsistent; there are no points of intersection.