Which describes the system of equations below? y = –6x − 2 y = 9/4x − 4/9 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Analyze Equations Relationship: Analyze the given system of equations to determine their relationship. The system of equations is: y = –6x − 2 y = 9/4x − 4/9 We need to check if the lines represented by these equations are parallel, intersecting, or coinciding.Compare Slopes: Compare the slopes of the two equations. The slope of the first equation y = –6x − 2 is -6. The slope of the second equation y = 9/4x − 4/9 is 9/4. Since the slopes are different, the lines are not parallel and they will intersect at some point.Determine Solution Type: Determine if the system has one solution or infinitely many solutions. Since the slopes are different, there is only one point of intersection. This means the system has one solution and is 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? $\newline$ $y = -6x - 2$ $\newline$ $y = \frac{9}{4}x - \frac{4}{9}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (C)consistent and independent

View step-by-step help

Home

Math Problems

Grade 8

Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -6x - 2

\newline

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

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Analyze Equations Relationship: Analyze the given system of equations to determine their relationship. $\newline$ The system of equations is: $\newline$ $y = -6x - 2$ $\newline$ $y = \frac{9}{4}x - \frac{4}{9}$ $\newline$ We need to check if the lines represented by these equations are parallel, intersecting, or coinciding.
Compare Slopes: Compare the slopes of the two equations. $\newline$ The slope of the first equation $y = -6x - 2$ is $-6$ . $\newline$ The slope of the second equation $y = \frac{9}{4}x - \frac{4}{9}$ is $\frac{9}{4}$ . $\newline$ Since the slopes are different, the lines are not parallel and they will intersect at some point.
Determine Solution Type: Determine if the system has one solution or infinitely many solutions. $\newline$ Since the slopes are different, there is only one point of intersection. This means the system has one solution and is consistent and independent.