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

Compare Slopes: We have the following system of equations: y = (3/8)x + 2 y = (3/8)x + 1/7 First, we need to compare the slopes of both equations to determine if they are the same. In y = (3/8)x + 2, the slope is 3/8. In y = (3/8)x + 1/7, the slope is also 3/8. Since both slopes are 3/8, the lines are parallel or the same line.Compare Y-Intercepts: Next, we compare the y-intercepts of both equations to determine if they are the same. In y = (3/8)x + 2, the y-intercept is 2. In y = (3/8)x + 1/7, the y-intercept is 1/7. Since 2 is not equal to 1/7, the y-intercepts are different.Conclusion: Since the slopes of the two equations are the same but the y-intercepts are different, the lines are parallel and will never intersect. This means that there are no solutions where the two equations are true at the same time. Therefore, the system of equations is inconsistent.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 1

Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{3}{8}x + 2

\newline

y = \frac{3}{8}x + \frac{1}{7}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

\newline

Compare Slopes: We have the following system of equations: $\newline$ $y = \frac{3}{8}x + 2$ $\newline$ $y = \frac{3}{8}x + \frac{1}{7}$ $\newline$ First, we need to compare the slopes of both equations to determine if they are the same. $\newline$ In $y = \frac{3}{8}x + 2$ , the slope is $\frac{3}{8}$ . $\newline$ In $y = \frac{3}{8}x + \frac{1}{7}$ , the slope is also $\frac{3}{8}$ . $\newline$ Since both slopes are $\frac{3}{8}$ , the lines are parallel or the same line.
Compare Y-Intercepts: Next, we compare the y-intercepts of both equations to determine if they are the same. $\newline$ In $y = \frac{3}{8}x + 2$ , the y-intercept is $2$ . $\newline$ In $y = \frac{3}{8}x + \frac{1}{7}$ , the y-intercept is $\frac{1}{7}$ . $\newline$ Since $2$ is not equal to $\frac{1}{7}$ , the y-intercepts are different.
Conclusion: Since the slopes of the two equations are the same but the $y$ -intercepts are different, the lines are parallel and will never intersect. This means that there are no solutions where the two equations are true at the same time. Therefore, the system of equations is inconsistent.