Which describes the system of equations below? y = 10/3x − 3/4 y = –2/7x − 8/3 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Analyze System of Equations: Analyze the given system of equations to determine if they are consistent, inconsistent, or dependent. The system of equations is: y = 10/3x - 3/4 y = -2/7x - 8/3 To determine the type of system, we need to look at the slopes and y-intercepts of the two lines represented by these equations.Identify Slopes and Intercepts: Identify the slopes and y-intercepts of the two lines. For the first equation, y = 10/3x - 3/4, the slope (m1) is 10/3 and the y-intercept (b1) is -3/4. For the second equation, y = -2/7x - 8/3, the slope (m2) is -2/7 and the y-intercept (b2) is -8/3. Since the slopes m1 and m2 are different (10/3 ≠ -2/7), the lines are not parallel and therefore cannot be dependent.Determine Consistency: Determine if the system is consistent or inconsistent. Since the slopes are different, the lines will intersect at exactly one point. This means the system has one solution and is therefore consistent and independent.Choose Correct Answer: Choose the correct answer based on the analysis. The system of equations is consistent and independent because the lines intersect at exactly one point.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which describes the system of equations below? $\newline$ $y = \frac{10}{3}x - \frac{3}{4}$ $\newline$ $y = -\frac{2}{7}x - \frac{8}{3}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent $\newline$

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 = \frac{10}{3}x - \frac{3}{4}

\newline

y = -\frac{2}{7}x - \frac{8}{3}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

\newline

Analyze System of Equations: Analyze the given system of equations to determine if they are consistent, inconsistent, or dependent. $\newline$ The system of equations is: $\newline$ $y = \frac{10}{3}x - \frac{3}{4}$ $\newline$ $y = -\frac{2}{7}x - \frac{8}{3}$ $\newline$ To determine the type of system, we need to look at the slopes and $y$ -intercepts of the two lines represented by these equations.
Identify Slopes and Intercepts: Identify the slopes and $y$ -intercepts of the two lines. $\newline$ For the first equation, $y = \frac{10}{3}x - \frac{3}{4}$ , the slope ( $m_1$ ) is $\frac{10}{3}$ and the $y$ -intercept ( $b_1$ ) is $-\frac{3}{4}$ . $\newline$ For the second equation, $y = -\frac{2}{7}x - \frac{8}{3}$ , the slope ( $m_2$ ) is $-\frac{2}{7}$ and the $y$ -intercept ( $y = \frac{10}{3}x - \frac{3}{4}$ $1$ ) is $y = \frac{10}{3}x - \frac{3}{4}$ $2$ . $\newline$ Since the slopes $m_1$ and $m_2$ are different ( $y = \frac{10}{3}x - \frac{3}{4}$ $5$ ), the lines are not parallel and therefore cannot be dependent.
Determine Consistency: Determine if the system is consistent or inconsistent. $\newline$ Since the slopes are different, the lines will intersect at exactly one point. This means the system has one solution and is therefore consistent and independent.
Choose Correct Answer: Choose the correct answer based on the analysis. $\newline$ The system of equations is consistent and independent because the lines intersect at exactly one point.