Which describes the system of equations below? y = –7/5x + 7/10 y = 4/3x − 9/5 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Compare Slopes and Intercepts: To determine the type of system represented by the two equations, we need to compare their slopes and y-intercepts. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. For the first equation, y = –7/5x + 7/10, the slope (m1) is –7/5 and the y-intercept (b1) is 7/10. For the second equation, y = 4/3x − 9/5, the slope (m2) is 4/3 and the y-intercept (b2) is –9/5.Calculate Slopes and Intercepts: We compare the slopes of the two lines. If the slopes are equal, the lines are either the same line (infinite solutions, consistent and dependent) or parallel (no solutions, inconsistent). If the slopes are different, the lines intersect at one point (one solution, consistent and independent). m1 = –7/5 and m2 = 4/3. Since –7/5 is not equal to 4/3, the slopes are different.Determine Type of System: Because the slopes are different, the lines will intersect at exactly one point. This means the system of equations has one solution and is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = -\frac{7}{5}x + \frac{7}{10}$ $\newline$ $y = \frac{4}{3}x - \frac{9}{5}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and independent $\newline$ (C)consistent and dependent

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Grade 8

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

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

\newline

y = \frac{4}{3}x - \frac{9}{5}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Compare Slopes and Intercepts: To determine the type of system represented by the two equations, we need to compare their slopes and y-intercepts. $\newline$ The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. $\newline$ For the first equation, $y = -\frac{7}{5}x + \frac{7}{10}$ , the slope ( $m_1$ ) is $-\frac{7}{5}$ and the y-intercept ( $b_1$ ) is $\frac{7}{10}$ . $\newline$ For the second equation, $y = \frac{4}{3}x - \frac{9}{5}$ , the slope ( $m_2$ ) is $m$ $0$ and the y-intercept ( $m$ $1$ ) is $m$ $2$ .
Calculate Slopes and Intercepts: We compare the slopes of the two lines. If the slopes are equal, the lines are either the same line (infinite solutions, consistent and dependent) or parallel (no solutions, inconsistent). If the slopes are different, the lines intersect at one point (one solution, consistent and independent).
$m_1 = \frac{-7}{5}$ and $m_2 = \frac{4}{3}$ . Since $\frac{-7}{5}$ is not equal to $\frac{4}{3}$ , the slopes are different.
Determine Type of System: Because the slopes are different, the lines will intersect at exactly one point. This means the system of equations has one solution and is consistent and independent.