Which describes the system of equations below? y = 5x + 6 y = 8/5x + 3/4 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Identify slopes of equations: We have the following system of equations: y = 5x + 6 y = (8/5)x + 3/4 Identify whether the slopes of both the equations are the same. In y = 5x + 6, the slope is 5. In y = (8/5)x + 3/4, the slope is 8/5. No, the slopes of both the equations are not the same.Determine intersection point: Since the slopes are different, the lines represented by these equations are not parallel and will intersect at exactly one point. This means the system of equations has one unique solution.Classify system of equations: A system of equations with one unique solution is considered consistent and independent. Therefore, the correct choice that describes the system of equations is (C) 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? $\newline$ $y = 5x + 6$ $\newline$ $y = \frac{8}{5}x + \frac{3}{4}$ $\newline$ 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 = 5x + 6

\newline

y = \frac{8}{5}x + \frac{3}{4}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = 5x + 6$ $\newline$ $y = \frac{8}{5}x + \frac{3}{4}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 5x + 6$ , the slope is $5$ . $\newline$ In $y = \frac{8}{5}x + \frac{3}{4}$ , the slope is $\frac{8}{5}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine intersection point: Since the slopes are different, the lines represented by these equations are not parallel and will intersect at exactly one point. $\newline$ This means the system of equations has one unique solution.
Classify system of equations: A system of equations with one unique solution is considered consistent and independent. Therefore, the correct choice that describes the system of equations is (C) consistent and independent.