Which describes the system of equations below? y = 1/5x + 8 y = –3/7x + 1/2 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Analyze slopes: Analyze the slopes of both equations. The first equation is y = (1/5)x + 8, which has a slope of 1/5. The second equation is y = (−3/7)x + 1/2, which has a slope of −3/7. Since the slopes are different (1/5 ≠ −3/7), the lines are not parallel and will intersect at one point.Check y-intercepts: Determine if the y-intercepts are the same. The first equation has a y-intercept of 8. The second equation has a y-intercept of 1/2. Since the y-intercepts are different (8 ≠ 1/2), the lines intersect at a point that is not on the y-axis.Conclude system type: Conclude the type of system based on the slopes and y-intercepts. Since the slopes are different and the y-intercepts are different, the system of equations will have one unique solution where the two lines intersect. This means the system is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = \frac{1}{5}x + 8$ $\newline$ $y = -\frac{3}{7}x + \frac{1}{2}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (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{1}{5}x + 8

\newline

y = -\frac{3}{7}x + \frac{1}{2}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Analyze slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = \frac{1}{5}x + 8$ , which has a slope of $\frac{1}{5}$ . $\newline$ The second equation is $y = \left(−\frac{3}{7}\right)x + \frac{1}{2}$ , which has a slope of $−\frac{3}{7}$ . $\newline$ Since the slopes are different $\left(\frac{1}{5} \neq −\frac{3}{7}\right)$ , the lines are not parallel and will intersect at one point.
Check y-intercepts: Determine if the y-intercepts are the same. $\newline$ The first equation has a y-intercept of $8$ . $\newline$ The second equation has a y-intercept of $\frac{1}{2}$ . $\newline$ Since the y-intercepts are different ( $8 \neq \frac{1}{2}$ ), the lines intersect at a point that is not on the y-axis.
Conclude system type: Conclude the type of system based on the slopes and $y$ -intercepts. $\newline$ Since the slopes are different and the $y$ -intercepts are different, the system of equations will have one unique solution where the two lines intersect. This means the system is consistent and independent.