Which describes the system of equations below? y = –x + 10 y = –5/8x − 4/5 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. The first equation is y = –x + 10, which has a slope of -1. The second equation is y = –5/8x – 4/5, which has a slope of -5/8. Since the slopes are different (-1 ≠ -5/8), the lines are not parallel and will intersect at one point.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.Dependent or Independent: Determine if the system is dependent or independent. Because the lines intersect at exactly one point, they are not the same line, and thus the system is 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? $\newline$ $y = -x + 10$ $\newline$ $y = -\frac{5}{8}x - \frac{4}{5}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (C)consistent and independent

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 = -x + 10

\newline

y = -\frac{5}{8}x - \frac{4}{5}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The first equation is $y = -x + 10$ , which has a slope of $-1$ . $\newline$ The second equation is $y = -\frac{5}{8}x - \frac{4}{5}$ , which has a slope of $-\frac{5}{8}$ . $\newline$ Since the slopes are different ( $-1 \neq -\frac{5}{8}$ ), the lines are not parallel and will intersect at one point.
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.
Dependent or Independent: Determine if the system is dependent or independent. Because the lines intersect at exactly one point, they are not the same line, and thus the system is independent.