Which describes the system of equations below? y = –2x − 6/7 y = 2/5x + 5/6 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes of equations: Analyze the slopes of both equations. The first equation is y = –2x – 6/7, which has a slope of –2. The second equation is y = 2/5x + 5/6, which has a slope of 2/5. Since the slopes are different, the lines are not parallel and will intersect at some point.Determine single solution: Determine if the system has a single solution. Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.Determine dependent or independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line; however, in this case, the lines have different slopes and different y-intercepts, so they cannot be the same line. Therefore, the system is independent.Choose system description: Choose the correct description of the system. The system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution. The correct choice is (B) consistent and independent.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which describes the system of equations below? $\newline$ $y = -2x - \frac{6}{7}$ $\newline$ $y = \frac{2}{5}x + \frac{5}{6}$ $\newline$ Choices: $\newline$ (A) inconsistent $\newline$ (B) consistent and independent $\newline$ (C) consistent and dependent

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 = -2x - \frac{6}{7}

\newline

y = \frac{2}{5}x + \frac{5}{6}

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and independent

\newline

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ The first equation is $y = -2x - \frac{6}{7}$ , which has a slope of $-2$ . $\newline$ The second equation is $y = \frac{2}{5}x + \frac{5}{6}$ , which has a slope of $\frac{2}{5}$ . $\newline$ Since the slopes are different, the lines are not parallel and will intersect at some point.
Determine single solution: Determine if the system has a single solution. $\newline$ Since the slopes are different, the lines will intersect at exactly one point. This means the system has a single solution and is therefore consistent.
Determine dependent or independent: Determine if the system is dependent or independent. A system is dependent if the equations represent the same line; however, in this case, the lines have different slopes and different $y$ -intercepts, so they cannot be the same line. Therefore, the system is independent.
Choose system description: Choose the correct description of the system. $\newline$ The system of equations is consistent because there is at least one solution, and it is independent because there is exactly one solution. The correct choice is (B) consistent and independent.