Which describes the system of equations below? y = 4/5x + 4 y = –3/10x − 3/10 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify slopes of equations: We have the system of equations: y = (4/5)x + 4 y = (-3/10)x - 3/10 Identify whether the slopes of both the equations are the same. In y = (4/5)x + 4, the slope is 4/5. In y = (-3/10)x - 3/10, the slope is -3/10. No, the slopes of both the equations are not the same. Determine if slopes are same: Since the slopes of the two equations are different, this means that the lines will intersect at exactly one point. This implies that the system of equations has a unique solution. Therefore, the system of equations 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? $\newline$ $y = \frac{4}{5}x + 4$ $\newline$ $y = -\frac{3}{10}x - \frac{3}{10}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (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 = \frac{4}{5}x + 4

\newline

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

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify slopes of equations: We have the system of equations: $\newline$ $y = \frac{4}{5}x + 4$ $\newline$ $y = \frac{-3}{10}x - \frac{3}{10}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = \frac{4}{5}x + 4$ , the slope is $\frac{4}{5}$ . $\newline$ In $y = \frac{-3}{10}x - \frac{3}{10}$ , the slope is $\frac{-3}{10}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine if slopes are same: Since the slopes of the two equations are different, this means that the lines will intersect at exactly one point. This implies that the system of equations has a unique solution. $\newline$ Therefore, the system of equations is consistent and independent.